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2.6 Table of ODEs solved using Series method

Table 2.515: Differential equations solved using series method

#

ODE

ODE classification

Solved?

400

y′=y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

401

y′=4y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

402

2y′+3y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

403

y′+2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

404

y′=xy

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

405

(x−2)y′+y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

406

(2x−1)y′+2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

407

2(x+1)y′+y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

408

(x−1)y′+2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

409

2(x−1)y′=3y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

410

y′′=y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

411

y′′=4y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

412

y′′+9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

413

y′′+y=x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

414

y′x+y=0

["first_order_ode_series_frobenius"]

✓

415

2y′x=y

["first_order_ode_series_frobenius"]

✓

416

x2y′+y=0

["unknown"]

✗

417

x3y′=2y

["unknown"]

✗

418

y′′+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

419

y′′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

420

y′′−2y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

421

y′′+y′−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

422

x2y′′+x2y′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

423

y′′=y′+y
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

424

y′=1+y2
i.c.

["first_order_ode_series_taylor"]

✓

426

(x2−1)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

427

(x2+2)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

428

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

429

(x2+1)y′′+6y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

430

(x2−3)y′′+2y′x=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

431

(x2−1)y′′−6y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

432

(x2+3)y′′−7y′x+16y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

433

(−x2+2)y′′−y′x+16y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

434

(x2−1)y′′+8y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

435

3y′′+y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

436

5y′′−2y′x+10y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

437

y′′−x2y′−3xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

438

y′′+x2y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

439

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

440

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

441

(x2+1)y′′+2y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

442

y′′+y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

443

y′′+(x−1)y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

444

(−x2+2x)y′′−6(x−1)y′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

445

(x2−6x+10)y′′−4(x−3)y′+6y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

446

(4x2+16x+17)y′′=8y
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

447

(x2+6x)y′′+(3x+9)y′−3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

448

y′′+(x+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

449

(x2−1)y′′+2y′x+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

450

y′′+x2y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

451

(x3+1)y′′+yx4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

452

y′′+y′x+(2x2+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

453

y′′+e−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

454

cos⁡(x)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

455

xy′′+y′sin⁡(x)+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

456

y′′−2y′x+2αy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

457

xy′′+(−x3+x)y′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

458

xy′′+x2y′+(ex−1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

459

x2y′′+cos⁡(x)y′+xy=0

["unknown"]

✗

460

3x3y′′+2x2y′+(−x2+1)y=0

["unknown"]

✗

461

x(x+1)y′′+2y′+3xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

462

x2(−x2+1)y′′+2y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

463

x2y′′+6y′sin⁡(x)+6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

464

(2x3+6x2)y′′+21y′x+9(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

465

(1−x)y′′+y′x+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

466

(1−x)2y′′+(2x−2)y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

467

(−x2+1)y′′−2y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

468

(x−2)3y′′+3(x−2)2y′+x3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

469

(x2−4)y′′+(x−2)y′+(x+2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

470

(x2−9)2y′′+(x2+9)y′+(x2+4)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

471

(x−2)2y′′−(x2−4)y′+(x+2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

472

x3(1−x)y′′+(3x+2)y′+xy=0

["unknown"]

✗

473

4xy′′+2y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

474

2xy′′+3y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

475

2xy′′−y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

476

3xy′′+2y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

477

2x2y′′+y′x−(2x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

478

2x2y′′+y′x−(−2x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

479

6x2y′′+7y′x−(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

480

3x2y′′+2y′x+x2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

481

2xy′′+(x+1)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

482

2xy′′+(−2x2+1)y′−4xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

483

xy′′+2y′+9xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

484

xy′′+2y′−4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

485

4xy′′+8y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

486

xy′′−y′+4x3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

487

4x2y′′−4y′x+(−4x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

488

2x2y′′+x(x+1)y′−(2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

489

(5x3+2x2)y′′+(−x2+3x)y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

490

2x2y′′+y′sin⁡(x)−cos⁡(x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

491

x2y′′+(3x−1)y′+y=0

["unknown"]

✗

492

x3y′′−y′x+y=0

["unknown"]

✗

493

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

494

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

495

x2y′′+y′x+(1−x)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

496

x(x−1)(x+1)2y′′+2x(x−3)(x+1)y′−2(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

497

x(1−x)y′′+(γ−(α+β+1)x)y′−αβy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

498

xy′′+(3−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

499

xy′′+(5−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

500

xy′′+(3x+5)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

501

5xy′′+(30+3x)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

502

xy′′−(x+4)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

503

2xy′′−(6+2x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

504

x2y′′+(3x2+2x)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

505

x(1−x)y′′−3y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

506

xy′′+y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

507

x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

508

x2y′′+(x2−3x)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

509

x2y′′+x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

510

x2y′′+(2x2−3x)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

511

x2y′′+x(x+1)y′−4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

512

x2y′′+y′x+(x2−94)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

513

x2y′′−x(x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

1042

y′=y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1043

y′=4y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1044

2y′+3y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1045

y′+2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1046

y′=x2y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1047

(x−2)y′+y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1048

(2x−1)y′+2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1049

2(x+1)y′=y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1050

(x−1)y′+2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1051

2(x−1)y′=3y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1052

y′′=y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1053

y′′=4y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1054

y′′+9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1055

y′′+y=x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1056

y′x+y=0

["first_order_ode_series_frobenius"]

✓

1057

2y′x=y

["first_order_ode_series_frobenius"]

✓

1058

x2y′+y=0

["unknown"]

✗

1059

x3y′=2y

["unknown"]

✗

1060

y′′+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1061

y′′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1062

y′′−2y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1063

y′′+y′−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1064

x2y′′+x2y′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

1066

(x2−1)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1067

(x2+2)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1068

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1069

(x2+1)y′′+6y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1070

(x2+1)y′′+2y′x=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1071

(x2−1)y′′−6y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1072

(x2+3)y′′−7y′x+16y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1073

(−x2+2)y′′−y′x+16y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1074

(x2−1)y′′+8y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1075

3y′′+y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1076

5y′′−2y′x+10y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1077

y′′−x2y′−3xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1078

y′′+x2y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1079

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1080

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1081

(x2+1)y′′+2y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1082

y′′+y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1083

y′′+(x−1)y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1084

(−x2+2x)y′′−6(x−1)y′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1085

(x2−6x+10)y′′−4(x−3)y′+6y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1086

(4x2+16x+17)y′′=8y
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1087

(x2+6x)y′′+(3x+9)y′−3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1088

y′′+(x+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1089

(x2−1)y′′+2y′x+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1090

y′′+x2y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1091

(x3+1)y′′+yx4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1092

y′′+y′x+(2x2+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1093

y′′+e−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1094

cos⁡(x)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1095

xy′′+y′sin⁡(x)+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1096

y′′−2y′x+2αy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1097

y′′=xy

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1361

y′′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1362

y′′−y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1363

y′′+k2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1364

(1−x)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1365

(x2+2)y′′−y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1366

y′′+y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1367

(x2+1)y′′−4y′x+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1368

(−x2+4)y′′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1369

(−x2+3)y′′−3y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1370

(1−x)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1371

2y′′+y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1372

y′′−y′x−y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1373

(x2+2)y′′−y′x+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1374

y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1375

(1−x)y′′+y′x−y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1376

y′′−2y′x+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1377

y′′−y′x−y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1378

(x2+2)y′′−y′x+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1379

y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1380

(−x2+4)y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1381

y′′+x2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1382

(1−x)y′′+y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1383

y′′+y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1384

y′′+y′sin⁡(x)+cos⁡(x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1385

x2y′′+(x+1)y′+3yln⁡(x)=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1386

y′′+x2y′+ysin⁡(x)=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1387

y′′+4y′+6xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1388

y′′+4y′+6xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1389

(x2−2x−3)y′′+y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1390

(x2−2x−3)y′′+y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1391

(x2−2x−3)y′′+y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1392

(x3+1)y′′+4y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1393

(x3+1)y′′+4y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1394

xy′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1395

(−x2+1)y′′−y′x+α2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1396

y′−y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1397

y′−xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1398

(1−x)y′=y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

1399

(−x2+1)y′′−2y′x+α(α+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1840

(x+2)y′′+y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1841

(3x2+1)y′′+3x2y′−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1842

(2x2+1)y′′+(2−3x)y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1843

(x2+1)y′′+(2−x)y′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1844

(3x2+1)y′′−2y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1845

xy′′+(4+2x)y′+(x+2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1846

x2y′′+2y′x−3xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1847

(2−x)y′′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1848

(x+1)y′′+2(x−1)2y′+3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1849

x2(1−x)y′′+x(x+4)y′+(2−x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1850

x2(x+1)y′′+x(2x+1)y′−(6x+4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1851

x2(x+1)y′′−x(−x2−6x+1)y′+(x2+6x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

1852

x2(3x+1)y′′+x(x2+12x+2)y′+2x(3+x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1853

x2(2x2+1)y′′+x(2x2+4)y′+2(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1854

x2(x2+2)y′′+2x(x2+5)y′+2(−x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1855

(x2+1)y′′+6y′x+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1856

(x2+1)y′′+2y′x−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1857

(x2+1)y′′−8y′x+20y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1858

(−x2+1)y′′−8y′x−12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1859

(2x2+1)y′′+7y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1860

(x2+1)y′′+2y′x+y4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1861

(−x2+1)y′′−5y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1862

(x2+1)y′′−10y′x+28y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1863

y′′+y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1864

y′′+2y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1865

(x2+1)y′′+y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1866

(2x2+1)y′′−9y′x−6y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1867

(8x2+1)y′′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1868

y′′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1869

y′′−(x−3)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1870

(2x2−4x+1)y′′+10(x−1)y′+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1871

(2x2−8x+11)y′′−16(x−2)y′+36y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1872

(3x2+6x+5)y′′+9(x+1)y′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1873

(x2−4)y′′−y′x−3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1874

y′′+(x−3)y′+3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1875

(3x2−6x+5)y′′+(x−1)y′+12y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1876

(4x2−24x+37)y′′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1877

(x2−8x+14)y′′−8(x−4)y′+20y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1878

(2x2+4x+5)y′′−20(x+1)y′+60y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1879

(x2+1)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1880

y′′−2y′x+2αy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1881

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1882

(−2x3+1)y′′−10x2y′−8xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1883

(x3+1)y′′+7x2y′+9xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1884

(−2x3+1)y′′+6x2y′+24xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1885

(−x3+1)y′′+15x2y′−36xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1886

(2x5+1)y′′+14x4y′+10x3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1887

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1888

y′′+x6y′+7x5y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1889

(x8+1)y′′−16x7y′+72x6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1890

(−x6+1)y′′−12x5y′−30yx4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1891

y′′+x5y′+6yx4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1892

(3x+1)y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1893

(2x2+x+1)y′′+(2+8x)y′+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1894

(−2x2+1)y′′+(2−6x)y′−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1895

(3x2+x+1)y′′+(2+15x)y′+12y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1896

(x+2)y′′+(x+1)y′+3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1897

(x2+3x+3)y′′+(6+4x)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1898

(x+4)y′′+(x+2)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1899

(2x2−3x+2)y′′−(4−6x)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1900

(2x2+3x)y′′+10(x+1)y′+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1901

(x2−x+1)y′′−(1−4x)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1902

(x+2)y′′+(x+2)y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1903

x2y′′−(6−7x)y′+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1904

(2x2+x+1)y′′+(1+7x)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1905

(3+x)y′′+(2x+1)y′−(2−x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1906

y′′+3y′x+(2x2+4)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1907

(2+4x)y′′−4y′−(6+4x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1908

(2x+1)y′′−(−2x+1)y′−(3−2x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1909

(5+2x)y′′−y′+(5+x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1910

(x+4)y′′−(4+2x)y′+(6+x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1911

(3x+2)y′′−y′x+2xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1912

(2x+3)y′′+3y′−xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1913

(2x+3)y′′−3y′−(x+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1914

(10−2x)y′′+(x+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1915

(7+x)y′′+(8+2x)y′+(5+x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1916

(6+4x)y′′+(2x+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1917

(βx2+αx+1)y′′+(δx+γ)y′+ϵy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1918

(2x2+3x+1)y′′+(6+8x)y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1919

(6x2−5x+1)y′′−(10−24x)y′+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1920

(4x2−4x+1)y′′−(8−16x)y′+8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1921

(x2+4x+4)y′′+(8+4x)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1922

(3x2+8x+4)y′′+(16+12x)y′+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1923

y′′+2y′x+(2x2+3)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1924

y′′−3y′x+(2x2+5)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1925

y′′+5y′x−(−x2+3)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1926

y′′−2y′x−(3x2+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1927

y′′+3y′x+(4x2+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1928

2y′′+5y′x+(2x2+4)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1929

3y′′+2y′x+(−x2+4)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1930

y′′+4y′x+(4x2+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1931

y′′+4y′x+(4x2+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1932

(x+1)y′′+x2y′+(2x+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1933

y′′+(x2+2x+1)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1934

(x2+1)y′′+(x2+2)y′+xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1935

(x+1)y′′+(2x2−3x+1)y′−(x−4)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1936

y′′+(3x2+12x+13)y′+(5+2x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1937

(3x2+2x+1)y′′+(−x2+2)y′+(x+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1938

(x2+4x+3)y′′−(−x2+4x+5)y′−(x+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1939

(x2+2x+1)y′′+(1−x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1940

(−2x2+x)y′′+(−x2+3x+1)y′+(x+2)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1941

(2x2−11x+16)y′′+(x2−6x+10)y′−(2−x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

1942

2x2(x2+x+1)y′′+x(11x2+11x+9)y′+(7x2+10x+6)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1943

(3+x)x2y′′+5x(x+1)y′−(1−4x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1944

x2(−x2+2)y′′−x(4x2+3)y′+(2x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1945

2x2(x2+x+1)y′′+x(5x2+3x+3)y′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

1946

3x2y′′+2x(−2x2+x+1)y′+(−8x2+2x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1947

x2(x2+3x+3)y′′+x(7x2+8x+5)y′−(−9x2−2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1948

4x2y′′+x(4x2+2x+7)y′−(−7x2−4x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1949

12x2(x+1)y′′+x(3x2+35x+11)y′−(−5x2−10x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1950

x2(10x2+x+5)y′′+x(48x2+3x+4)y′+(36x2+x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1951

8x2y′′−2x(−x2−4x+3)y′+(x2+6x+3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1952

18x2(x+1)y′′+3x(x2+11x+5)y′−(−5x2−2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1953

x(x2+x+3)y′′+(−x2+x+4)y′+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1954

10x2(2x2+x+1)y′′+x(66x2+13x+13)y′−(10x2+4x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1955

2x2y′′+x(2x+3)y′−(1−x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1956

(3+x)x2y′′+x(5+4x)y′−(−2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1957

2x2y′′+x(5+x)y′−(2−3x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1958

3x2y′′+x(x+1)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1959

2x2y′′−y′x+(−2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1960

9x2y′′+9y′x−(3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1961

3x2y′′+x(x+1)y′−(3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1962

2(3+x)x2y′′+x(1+5x)y′+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1963

x2(x+4)y′′−x(1−3x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1964

2x2y′′+5y′x+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1965

x2(4x+3)y′′+x(5+18x)y′−(1−12x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1966

6x2y′′+x(10−x)y′−(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1967

x2(8+x)y′′+x(3x+2)y′+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1968

x2(4x+3)y′′+x(11+4x)y′−(4x+3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1969

2x2(3x+2)y′′+x(4+11x)y′−(1−x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1970

x2(x+2)y′′+5x(1−x)y′−(2−8x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1971

x2(6+x)y′′+x(11+4x)y′+(2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1972

8x2y′′+x(x2+2)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1973

8x2(−x2+1)y′′+2x(−13x2+1)y′+(−9x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1974

x2(x2+1)y′′−2x(−x2+2)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1975

x(x2+3)y′′+(−x2+2)y′−8xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1976

4x2(−x2+1)y′′+x(−19x2+7)y′−(14x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1977

3x2(−x2+2)y′′+x(−11x2+1)y′+(−5x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1978

2x2(x2+2)y′′−x(−7x2+12)y′+(3x2+7)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1979

2x2(x2+2)y′′+x(7x2+4)y′−(−3x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1980

2x2(2x2+1)y′′+5x(6x2+1)y′−(−40x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1981

3x2(x2+1)y′′+5x(x2+1)y′−(−5x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1982

x(x2+1)y′′+(7x2+4)y′+8xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1983

x2(x2+2)y′′+x(x2+3)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1984

2x2(x2+1)y′′+x(8x2+3)y′−(−4x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1985

9x2y′′+3x(x2+3)y′−(−5x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1986

6x2y′′+x(6x2+1)y′+(9x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1987

x2(x2+8)y′′+7x(x2+2)y′−(−9x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1988

9x2(x2+1)y′′+3x(13x2+3)y′−(−25x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1989

4x2(x2+1)y′′+4x(6x2+1)y′−(−25x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1990

8x2(2x2+1)y′′+2x(34x2+5)y′−(−30x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1991

2x2(x+1)y′′−x(1−3x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1992

6x2(2x2+1)y′′+x(50x2+1)y′+(30x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1993

28x2(1−3x)y′′−7x(5+9x)y′+7(2+9x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1994

9x2(5+x)y′′+9x(5+9x)y′−(5−8x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1995

8x2(−x2+2)y′′+2x(−21x2+10)y′−(35x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1996

4x2(x2+3x+1)y′′−4x(−3x2−3x+1)y′+3(x2−x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

1997

3x2(x+1)2y′′−x(−11x2−10x+1)y′+(5x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1998

4x2(x2+2x+3)y′′−x(−15x2−14x+3)y′+(7x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

1999

x2(x2−2x+1)y′′−(3+x)xy′+(x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2000

2x2(x+2)y′′+5x2y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2001

x2(−x2+2)y′′−2x(2x2+1)y′+(−2x2+2)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2002

x2y′′−x(5−x)y′+(9−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2003

x2y′′−x(1−x)y′+(−x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2004

x2(2x2+x+1)y′′+x(7x2+6x+3)y′+(−3x2+6x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2005

x2(x2+2x+1)y′′+x(4x2+3x+1)y′−x(−2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2006

4x2(x2+x+1)y′′+12x2(x+1)y′+(3x2+3x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2007

x2(x2+x+1)y′′−x(−2x2−4x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2008

9x2y′′+3x(−2x2+3x+5)y′+(−14x2+12x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2009

x2y′′+x(x2+x+1)y′+x(2−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2010

x2(2x+1)y′′+x(3x2+14x+5)y′+(12x2+18x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2011

4x2y′′+2x(x2+x+4)y′+(3x2+5x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2012

16x2y′′+4x(2x2+x+6)y′+(18x2+5x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2013

9x2(x+1)y′′+3x(−x2+11x+5)y′+(−7x2+16x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2014

4x2y′′+(1+4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2015

36x2(−2x+1)y′′+24x(1−9x)y′+(1−70x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2016

x2(x+1)y′′−x(3−x)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2017

x2(−2x+1)y′′−x(5−4x)y′+(9−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2018

25x2y′′+x(15+x)y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2019

2x2(x+2)y′′+x2y′+(1−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2020

x2(9+4x)y′′+3y′x+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2021

x2y′′−x(3−2x)y′+(3x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2022

x2(1−4x)y′′+3x(1−6x)y′+(1−12x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2023

x2(2x+1)y′′+x(3+5x)y′+(−2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2024

2x2(x+1)y′′−x(6−x)y′+(8−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2025

x2(2x+1)y′′+x(5+9x)y′+(3x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2026

x2(−2x+1)y′′−x(5+4x)y′+(9+4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2027

x2(1+4x)y′′−x(1−4x)y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2028

x2(x+1)y′′+x(2x+1)y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2029

x2(1−x)y′′+x(7+x)y′+(9−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2030

x2y′′−x(−x2+1)y′+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2031

x2(x2+1)y′′−3x(−x2+1)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2032

4x2y′′+2x3y′+(3x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2033

x2(x2+1)y′′−x(−2x2+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2034

2x2(x2+2)y′′+7x3y′+(3x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2035

x2(x2+1)y′′−x(−4x2+1)y′+(2x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2036

4x2(x2+4)y′′+3x(3x2+8)y′+(−9x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2037

3x2(x2+3)y′′+x(11x2+3)y′+(5x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2038

4x2(4x2+1)y′′+32x3y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2039

9x2y′′−3x(−2x2+7)y′+(2x2+25)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2040

x2(2x2+1)y′′+x(7x2+3)y′+(−3x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2041

x2(x2+1)y′′+x(8x2+3)y′+(12x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2042

x2y′′−x(−x2+1)y′+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2043

x2(−2x2+1)y′′+x(−9x2+5)y′+(−3x2+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2044

x2(x2+2)y′′+x(−x2+14)y′+2(x2+9)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2045

x2(x2+1)y′′+x(7x2+3)y′+(8x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2046

x2(−2x+1)y′′+3y′x+(1+4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2047

x(x+1)y′′+(1−x)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2048

x2(1−x)y′′+x(3−2x)y′+(2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2049

4x2(x+1)y′′+4x2y′+(1−5x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2050

x2(1−x)y′′−x(3−5x)y′+(4−5x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2051

x2(x2+1)y′′−x(9x2+1)y′+(25x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2052

9x2y′′+3x(−x2+1)y′+(7x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2053

x(x2+1)y′′+(−x2+1)y′−8xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2054

4x2y′′+2x(−x2+4)y′+(7x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2055

4x2(x+1)y′′+8x2y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2056

9(3+x)x2y′′+3x(3+7x)y′+(4x+3)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2057

x2(−x2+2)y′′−x(3x2+2)y′+(−x2+2)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2058

16x2(x2+1)y′′+8x(9x2+1)y′+(49x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2059

x2(3x+4)y′′−x(4−3x)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2060

4x2(x2+3x+1)y′′+8x2(2x+3)y′+(9x2+3x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2061

x2(1−x)2y′′−x(−3x2+2x+1)y′+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2062

9x2(x2+x+1)y′′+3x(13x2+7x+1)y′+(25x2+4x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2063

2x2(x+2)y′′−x(4−7x)y′−(5−3x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2064

x2(−2x+1)y′′+x(8−9x)y′+(6−3x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2065

x2(x2+1)y′′+x(10x2+3)y′−(−14x2+15)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2066

x2(−2x2+1)y′′+x(−13x2+7)y′−14x2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2067

x2y′′−3y′x+(4x+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2068

xy′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2069

4x2(x+1)y′′+4x(2x+1)y′−(3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2070

x(x+1)y′′+y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2071

2x2(3x+2)y′′+x(4+21x)y′−(1−9x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2072

x2y′′+x(x+2)y′−(2−3x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2073

4x2y′′+4y′x−(9−x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2074

x2y′′+10y′x+(14+x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2075

4x2(x+1)y′′+4x(3+8x)y′−(5−49x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2076

x2(x+1)y′′−x(3+10x)y′+30xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2077

x2y′′+x(x+1)y′−3(3+x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2078

x2y′′+x(−2x+1)y′−(x+4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2079

x(x+1)y′′−4y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2080

x2(2x+1)y′′+x(9+13x)y′+(7+5x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2081

4x2(2x+1)y′′−2x(4−x)y′−(7+5x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2082

3(3+x)x2y′′−x(15+x)y′−20y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2083

x2(x+1)y′′+x(1−10x)y′−(9−10x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2084

x2(x+1)y′′+3x2y′−(6−x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2085

x2(2x+1)y′′−2x(3+14x)y′+(6+100x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2086

x2(x+1)y′′−x(6+11x)y′+(6+32x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2087

4x2(x+1)y′′+4x(1+4x)y′−(49+27x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2088

x2(2x+1)y′′−x(9+8x)y′−12xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2089

x2(x2+1)y′′−x(−2x2+7)y′+12y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2090

x2y′′−x(−x2+7)y′+12y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2091

xy′′−5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2092

x2y′′+x(2x2+1)y′−(−10x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2093

x2y′′−y′x−(−x2+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2094

4x2y′′+2(x2+8)xy′+(3x2+5)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2095

x2y′′+x(x2+1)y′−(−3x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2096

x2y′′+x(−2x2+1)y′−4(2x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2097

4x2y′′+8y′x−(−x2+35)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2098

9x2y′′−3x(2x2+11)y′+(10x2+13)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2099

x2y′′+x(−2x2+1)y′−4(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2100

x2y′′+x(−3x2+1)y′−4(−3x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2101

x2(x2+1)y′′+x(11x2+5)y′+24x2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2102

4x2(x2+1)y′′+8y′x−(−x2+35)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2103

x2(x2+1)y′′−x(−x2+5)y′−(25x2+7)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2104

x2(x2+1)y′′+x(2x2+5)y′−21y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2105

x2(2x2+1)y′′−x(x2+3)y′−2xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2106

4x2(x2+1)y′′+4x(x2+2)y′−(x2+15)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2413

y′′+y′t+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2414

y′′−ty=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2415

(t2+2)y′′−y′t−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2416

y′′−t3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2417

t(2−t)y′′−6(t−1)y′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2418

y′′+t2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2419

y′′−t3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2420

y′′+(t2+2t+1)y′−(4+4t)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2421

y′′−2y′t+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2422

(−t2+1)y′′−2y′t+α(α+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2423

(−t2+1)y′′−y′t+α2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2424

y′′+t3y′+3t2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2425

y′′+t3y′+3t2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2426

(1−t)y′′+y′t+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2427

y′′+y′+ty=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2428

y′′+y′t+ety=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2429

y′′+y′+ety=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2430

y′′+y′+e−ty=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2441

t(t−2)2y′′+y′t+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2442

t(t−2)2y′′+y′t+y=0

["unknown"]

✗

2443

sin⁡(t)y′′+cos⁡(t)y′+yt=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2444

(et−1)y′′+ety′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2445

(−t2+1)y′′+y′sin⁡(1+t)+y=0

["unknown"]

✗

2446

t3y′′+sin⁡(t3)y′+ty=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2447

2t2y′′+3y′t−(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2448

2ty′′+(1−2t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2449

2ty′′+(1+t)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2450

2t2y′′−y′t+(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2451

4ty′′+3y′−3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2452

2t2y′′+(t2−t)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2453

t3y′′−y′t−(t2+54)y=0

["unknown"]

✗

2454

t2y′′+(−t2+t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2455

ty′′−(t2+2)y′+ty=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2456

t2y′′+(−t2+3t)y′−ty=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2457

t2y′′+t(1+t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2458

ty′′−(t+4)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2459

t2y′′+(t2−3t)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2460

t2y′′+y′t−(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2461

ty′′+y′t+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2462

ty′′+(−t2+1)y′+4ty=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2463

t2y′′+y′t+t2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2464

t2y′′+y′t+(t2−v2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2465

ty′′+(1−t)y′+λy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2466

2sin⁡(t)y′′+(1−t)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2467

t2y′′+y′t+(1+t)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2468

ty′′+y′−4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2469

t2y′′−t(1+t)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2470

t2y′′+y′t+(t2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2471

ty′′+3y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2611

y′′+y′t+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2612

y′′−ty=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2613

(t2+2)y′′−y′t−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2614

y′′−t3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2615

t(2−t)y′′−6(t−1)y′−4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2616

y′′+t2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2617

y′′−t3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2618

y′′+(t2+2t+1)y′−(4+4t)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2619

y′′−2y′t+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2620

(−t2+1)y′′−2y′t+α(α+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2621

(−t2+1)y′′−y′t+α2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2622

y′′+t3y′+3t2y=et
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2623

(1−t)y′′+y′t+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2624

y′′+y′+ty=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2625

y′′+y′t+ety=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2626

y′′+y′+ety=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2627

y′′+y′+e−ty=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

2638

t(t−2)2y′′+y′t+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2639

t(t−2)2y′′+y′t+y=0

["unknown"]

✗

2640

sin⁡(t)y′′+cos⁡(t)y′+yt=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2641

(et−1)y′′+ety′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2642

(−t2+1)y′′+y′sin⁡(1+t)+y=0

["unknown"]

✗

2643

t3y′′+sin⁡(t2)y′+ty=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2644

2t2y′′+3y′t−(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2645

2ty′′+(1−2t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2646

2ty′′+(1+t)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2647

2t2y′′−y′t+(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2648

4ty′′+3y′−3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2649

2t2y′′+(t2−t)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2650

t2y′′−y′t−(t2+54)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2651

t2y′′+(−t2+t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2652

ty′′−(t2+2)y′+ty=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2653

t2y′′+(−t2+3t)y′−ty=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2654

t2y′′+t(1+t)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2655

ty′′−(t+4)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2656

t2y′′+(t2−3t)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2657

t2y′′+y′t−(1+t)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2658

ty′′+y′t+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2659

t2y′′+(−t2+1)y′+4ty=0

["unknown"]

✗

2660

t2y′′+y′t+t2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2661

t2y′′+y′t+(t2−v2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2662

ty′′+(1−t)y′+λy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2663

t(1−t)y′′+(γ−(α+β+1)t)y′−αβy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2664

2sin⁡(t)y′′+(1−t)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

2665

t2y′′+y′t+(1+t)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

2666

ty′′+y′−4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2667

t2y′′−t(1+t)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

2668

t2y′′+y′t+(t2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2669

ty′′+3y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

2670

t2y′′+tp(t)y′+q(t)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3335

y′=1−y
i.c.

["first_order_ode_series_taylor"]

✓

3336

y′=xy−x2
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

3337

y′=x2y2
i.c.

["first_order_ode_series_taylor"]

✓

3338

y′=3x+yx
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

3339

y′=ln⁡(xy)
i.c.

["first_order_ode_series_taylor"]

✓

3340

y′=1+y2
i.c.

["first_order_ode_series_taylor"]

✓

3341

y′=x2+y2
i.c.

["first_order_ode_series_taylor"]

✓

3342

y′=xy+1
i.c.

["first_order_ode_series_taylor"]

✓

3343

y′=cos⁡(x)+sin⁡(y)
i.c.

["first_order_ode_series_taylor"]

✓

3344

y′′−y=sin⁡(x)
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3345

y′′−2y=e2x
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3346

y′′+2yy′=0
i.c.

["second_order_ode_series_taylor"]

✓

3347

y′′=sin⁡(y)
i.c.

["second_order_ode_series_taylor"]

✓

3348

y′′+y′22−y=0
i.c.

["second_order_ode_series_taylor"]

✓

3349

y′′=sin⁡(xy)
i.c.

["second_order_ode_series_taylor"]

✓

3350

y′′=cos⁡(xy)
i.c.

["second_order_ode_series_taylor"]

✓

3351

2xy′′+5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3352

3x(3x+2)y′′−4y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3353

x2(x+4)y′′+7y′x−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3354

2x2y′′+(−x2+x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3355

2x2y′′+5y′x+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3356

9x2y′′+(3x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3357

(x3+2x2)y′′−y′x+(1−x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3358

2x2y′′−3(x2+x)y′+(3x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3359

3x2y′′+(−x2+5x)y′+(2x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3360

4x2y′′+x(x2−4)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3361

4x2y′′−3(x2+x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3362

9x2y′′+9(−x2+x)y′+(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3363

4x2(1−x)y′′+3x(2x+1)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3364

2x2(1−3x)y′′+5y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3365

4x2(x+1)y′′−5y′x+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3366

x2(x+4)y′′+x(x−1)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3367

(8−x)x2y′′+6y′x−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3368

2x2y′′+x(x2+1)y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3369

2x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3370

3x2y′′+2y′x+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3371

x3(x2+3)y′′+5y′x−(x+1)y=0

["unknown"]

✗

3372

2xy′′−(x3+1)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3373

xy′′+y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3374

xy′′+y′+2xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3375

x2y′′−3y′x+4(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3376

x2y′′−x(x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3377

x2y′′−x(2x+3)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3378

x2(−x2+1)y′′−5y′x+9y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3379

x2y′′+x(x2−1)y′+(−x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3380

x2y′′+x(2x−1)y′+x(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3381

x2y′′−x2y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3382

x2y′′+2x2y′−(3x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3383

x2(1−x)y′′+x(x+1)y′−9y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3384

(−x2+x)y′′−3y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3385

x2y′′+x(x−7)y′+(x+12)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3386

x2(x+1)y′′+x(x−4)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3387

x2y′′+x(−x2+3)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3388

xy′′+3y′−y=x

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3389

xy′′+3y′−y=x

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3390

xy′′+y′−2xy=x2

["second_order_ode_series_frobenius_repeated_roots"]

✓

3391

xy′′−y′x+y=x3

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3392

(−2x+1)y′′+4y′x−4y=x2−x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3393

x2y′′+y′x+(x+12)y=x2+x

["second_order_ode_series_frobenius_complex_roots"]

✓

3394

x2(x+1)y′′+x(x2+3)y′+y=−2x2+x

["second_order_ode_series_frobenius_repeated_roots"]

✓

3395

3x2(x+1)y′′+x(5−x)y′+(2x2−1)y=−x3+x

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3396

9x2y′′+(3x+2)y=x4+x2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3397

9x2y′′+10y′x+y=x−1

["second_order_ode_series_frobenius_complex_roots"]

✓

3398

2x2y′′+(−x2+x)y′−y=x3+1

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3399

(−x2+1)y′′+2y′x−2y=6(−x2+1)2

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3400

(x2+2x)y′′−(2x+2)y′+2y=x2(x+2)2

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3401

2x2y′′+5y′x+(x+1)y=x(x2+x+1)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3402

(x3+2x2)y′′−y′x+(1−x)y=x2(x+1)2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3501

(−z2+1)y′′−3zy′+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3502

4zy′′+2(1−z)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3503

zy′′−2y′+9z5y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3504

f′′+2(z−1)f′+4f=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3505

z2y′′−3zy′2+(1+z)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

3506

zy′′−2y′+yz=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

3507

y′′−2zy′−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3508

z(1−z)y′′+(1−z)y′+λy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3509

zy′′+(2z−3)y′+4yz=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3510

(z2+5z+6)y′′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3511

(z2+5z+7)y′′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3512

y′′+yz3=0

["unknown"]

✗

3513

zy′′+(1−z)y′+λy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

3514

(−z2+1)y′′−zy′+m2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3986

y′′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3987

y′′+2y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3988

y′′−2y′x−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3989

y′′−x2y′−2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3990

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3991

y′′+y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3992

y′′−x2y′−3xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3993

y′′+2x2y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3994

(x2−3)y′′−3y′x−5y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3995

(x2+1)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3996

(−4x2+1)y′′−20y′x−16y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3997

(x2−1)y′′−6y′x+12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3998

y′′+2y′+4xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

3999

y′′+y′x+(x+2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4000

y′′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4001

xy′′−(x−1)y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4002

(2x2+1)y′′+7y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4003

4y′′+y′x+4y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4004

y′′+2x2y′+xy=2cos⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4005

y′′+y′x−4y=6ex

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4006

y′′+y′1−x+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4007

x2y′′+xy′(−x2+1)2+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

4008

(x−2)2y′′+(x−2)exy′+4yx=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4009

y′′+2y′x(x−3)−yx3(3+x)=0

["unknown"]

✗

4010

x2y′′+x(1−x)y′−7y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4011

4x2y′′+xexy′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4012

4xy′′−y′x+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4013

x2y′′−xcos⁡(x)y′+5e2xy=0

["second_order_ode_series_frobenius_complex_roots"]

✓

4014

4x2y′′+3y′x+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4015

6x2y′′+x(1+18x)y′+(1+12x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4016

x2y′′+y′x−(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4017

2xy′′+y′−2xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4018

3x2y′′−x(8+x)y′+6y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4019

2x2y′′−x(2x+1)y′+2(4x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4020

x2y′′+x(1−x)y′−(5+x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4021

3x2y′′+x(3x+7)y′+(1+6x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4022

x2y′′+y′x+(1−x)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

4023

3x2y′′+x(3x2+1)y′−2xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4024

4x2y′′−4x2y′+(2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4025

x2y′′+x(3−2x)y′+(−2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4026

x2y′′−(3+x)xy′+(4−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4027

x2y′′+x(3−x)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4028

x2y′′+y′x−(x+4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4029

x2y′′−(−x2+x)y′+(x3+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4030

x2y′′−(25−1)xy′+(194−3x2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4031

x2y′′+(−2x5+9x)y′+(10x4+5x2+25)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

4032

x2y′′+(4x+12x2−13x3)y′−7y4=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4033

x2y′′+x2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4034

x2y′′+x(x−3)y′+(4−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4035

4x2y′′+2x2y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4036

x2y′′+xcos⁡(x)y′−2yex=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4037

x2y′′+x2y′−(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4038

x2y′′+2x2y′+(x−34)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4039

x2y′′+y′x+(2x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4040

x2y′′+x3y′−(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4041

x2(x2+1)y′′+7xexy′+9(1+tan⁡(x))y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4042

x2(x+1)y′′+x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4043

x2y′′+3y′x+(1−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4044

xy′′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4045

x2y′′+x(x2+6)y′+6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4046

x2y′′+x(1−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4047

4x2y′′+(1−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4048

xy′′+y′−2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4049

x2y′′+y′x−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4050

x2y′′−(3+x)xy′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4051

x2y′′−x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4052

x2y′′−x2y′−(3x+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4053

x2y′′+x(5−x)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4054

4x2y′′+4x(1−x)y′+(2x−9)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4055

x2y′′+2x(x+2)y′+2(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4056

x2y′′−x(1−x)y′+(1−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4057

4x2y′′+4x(2x+1)y′+(4x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4058

4x2y′′−(4x+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4059

xy′′−y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4060

x2y′′+x(x+4)y′+(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4061

x2y′′+y′x+(x2−94)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4062

xy′′−y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4063

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4064

y′′−x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4065

(−x2+1)y′′−6y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4066

xy′′+y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4067

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4068

2xy′′+5(−2x+1)y′−5y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4069

xy′′+y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4070

(4x2+1)y′′−8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4071

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4072

4xy′′+3y′+3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4073

x2y′′+3y′x2−(x+1)y2=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4074

x2y′′−x(2−x)y′+(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4075

x2y′′−3y′x+4(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4076

y′′+(1−34x2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4178

y′′+yx2=0

["second_order_ode_series_frobenius_complex_roots"]

✓

4179

y′′−(−3x2+x)y′2x3+2x2+y2x3+2x2=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4180

y′′+(1−1x)y′−yx=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4181

y′′+2y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4182

y′′−2y′+(14x2−1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4183

y′′−(x2+4x+2)((1−x)y′+y)x(−x2+2)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4184

y′′−3y′x(1−x)+2yx(1−x)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4185

y′′+(1−x)y′2x−y4x=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4186

y′′−y′2x+y4x=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4187

y′′−y′x+(1+1x2)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4188

y′′+(1−5x)y′−x2+x−4y−x2+x=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4189

y′′+(x−1)y′x(x+1)−yx(x+1)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4588

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4589

(x2+1)y′′+4y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4590

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4591

(−x2+1)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4592

y′′−2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4593

y′′−2x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4594

(x2−1)y′′+(4x−1)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4595

y′′+(cos⁡(x)+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4596

y′′+y′sin⁡(x)+cos⁡(x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

4597

xy′′+y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4598

xy′′+(1−x)y′+ky=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4599

x2y′′+(−2x2+x)y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

4600

x2y′′−(x2+2x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4601

x2y′′+(12x+x2)y′+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

4602

x2y′′+(−x2+x)y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4603

x2y′′+2y′x−(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4604

xy′′−2y′x−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4605

xy′′+2y′−xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4606

x2y′′−x2y′+2(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

4607

xy′′+y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6040

xy′′+(x+n)y′+(n+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6041

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6042

2x2y′′−y′x+(−x2+1)y=x2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6043

xy′′+2y′+a3x2y=2

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6044

y′′+ax2y=x+1

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6045

x4y′′+y′x+y=0

["unknown"]

✗

6046

x2y′′+(2x2+x)y′−4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6047

(−x2+x)y′′+3y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6048

(4x3−14x2−2x)y′′−(6x2−7x+1)y′+(6x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6049

x2y′′+x2y′+(x−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6050

x2y′′−x2y′+(x−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6051

x2(1−4x)y′′+((1−n)x−(6−4n)x2)y′+n(1−n)xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6052

x2y′′+(x2+x)y′+(x−9)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6053

(a2+x2)y′′+y′x−n2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6054

(−x2+1)y′′−y′x+a2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6055

xy′′+y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6056

xy′′+y′+pxy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6057

xy′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6058

x3y′′−(2x−1)y=0

["unknown"]

✗

6059

x2y′′+x(x+1)y′+(3x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6060

(−x2+x)y′′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6061

x(−x2+1)y′′+(−3x2+1)y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6062

y′′+ayx3/2=0

["unknown"]

✗

6063

x2y′′−(x2+4x)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6064

x(−x2+1)y′′+(−x2+1)y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6065

4x(1−x)y′′−4y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6066

x3y′′+y=x3/2

["unknown"]

✗

6067

2x2y′′−(3x+2)y′+(2x−1)yx=x

["unknown"]

✗

6068

(−x2+x)y′′+3y′+2y=3x2

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6069

x(1−x)y′′+(32−2x)y′−y4=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6070

2x(1−x)y′′+y′x−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6071

2x(1−x)y′′+(1−11x)y′−10y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6072

x(1−x)y′′+(−2x+1)y′3+20y9=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6073

2x(1−x)y′′+y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6074

4y′′+3(−x2+2)y(−x2+1)2=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6236

y′x=xy+y

["first_order_ode_series_frobenius"]

✓

6238

y′=3x2y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6240

y′x=y

["first_order_ode_series_frobenius"]

✓

6242

y′′=−4y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6244

y′′=y

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6246

y′′−2y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6248

x2y′′−3y′x+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6250

(x2+2x)y′′−2(x+1)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6252

(x2+1)y′′−2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6254

y′′−4y′x+(4x2−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6345

(x+1)y′′−x2y′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6346

x2y′′+3y′−xy=0

["unknown"]

✗

6347

(x2−2)y′′+2y′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6348

(x2+x)y′′+3y′−6xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6349

(t2−t−2)x′′+(1+t)x′−(t−2)x=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6350

(x2−1)y′′+(1−x)y′+(x2−2x+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6351

sin⁡(x)y′′+cos⁡(x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6352

exy′′−(x2−1)y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6353

sin⁡(x)y′′−yln⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6354

y′+(x+2)y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6355

y′−y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6356

z′−x2z=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6357

(x2+1)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6358

y′′+(x−1)y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6359

y′′−2y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6360

w′′−x2w′+w=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6361

(2x−3)y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6362

(x+1)y′′−3y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6363

y′′−y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6364

(x2+x+1)y′′−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6365

(x2−5x+6)y′′−3y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6366

y′′−y′tan⁡(x)+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6367

(x3+1)y′′−y′x+2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6368

y′+2(x−1)y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6369

y′−2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6370

(x2−2x)y′′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6371

x2y′′−y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6372

x2y′′−y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6373

y′′+(3x−1)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6374

x′+sin⁡(t)x=0
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6375

y′−yex=0
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6376

(x2+1)y′′−exy′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6377

y′′+y′t+ety=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6378

y′′−e2xy′+cos⁡(x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6379

y′−xy=sin⁡(x)

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6380

w′+wx=ex

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6381

z′′+xz′+z=x2+2x+1

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6382

y′′−2y′x+3y=x2

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6383

(x2+1)y′′−y′x+y=cos⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6384

y′′−y′x+2y=cos⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6385

(−x2+1)y′′−y′+y=tan⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6386

y′′−ysin⁡(x)=cos⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6387

(−x2+1)y′′−2y′x+n(n+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6559

(x+1)y′′+y′x+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6560

x3y′′+y=0

["unknown"]

✗

6561

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6562

y′′−2y′x−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6563

y′′+x2y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6564

y′′−x2y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6565

y′′+2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6566

(x2−1)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6567

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6568

y′′−2y′x+x2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6792

(1−x)y′=x2−y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6793

y′x=1−x+2y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6795

y′=2x2+3y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6796

(x+1)y′=x2−2x+y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6797

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6798

y′′+2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6799

y′′−y′x+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6800

(−x2+1)y′′−2y′x+p(p+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6801

y′′+x2y=x2+x+1

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6802

2(x3+x2)y′′−(−3x2+x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6803

4xy′′+2(1−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6804

2x2y′′−y′x+(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6805

xy′′+y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6806

x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6807

xy′′−2y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6808

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6809

x2(x+1)y′′+x(x+1)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6810

2xy′′+y′−y=x+1

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6811

2x3y′′+x2y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6812

x3y′′+(x2+x)y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6813

z′′+tz′+(t2−19)z=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6814

x(−x2+2)y′′−(x2+4x+2)((1−x)y′+y)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6815

x2(x+1)y′′−(2x+1)(y′x−y)=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6816

x3(x+1)y′′′−(2+4x)x2y′′+(4+10x)xy′−(4+12x)y=0

["unknown"]

✗

6817

x3(x2+1)y′′′−(4x2+2)x2y′′+(10x2+4)xy′−(12x2+4)y=0

["unknown"]

✗

6818

2x2(2−x)y′′−x(4−x)y′+(3−x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6819

x2(1−x)y′′+(5x−4)xy′+(6−9x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6820

xy′′+(4x2+1)y′+4x(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6821

x2y′′+4(x+a)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6822

xy′′+(x3+1)y′+bxy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6823

(x−1)(x−2)y′′+(4x−6)y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6824

y′′−2y′x+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6825

y′′−2y′x+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6826

(−x2+1)y′′−2y′x+12y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6827

y′′=(x−1)y
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6828

x(x+2)y′′+2(x+1)y′−2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6829

xy′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6830

y′′+(ex−1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6831

x(1−x)y′′−3y′x−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6832

2xy′′−y′+x2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6833

sin⁡(x)y′′−2cos⁡(x)y′−ysin⁡(x)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6834

y′′−x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6835

x(x+2)y′′+(x+1)y′−4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6836

xy′′+(12−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6837

x2y′′+y′x+(x2+14)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

6838

x2y′′+y′x+(x2+94)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

6839

x2y′′+y′x+(x2+254)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

6840

(x−1)y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6841

y′+xy=cos⁡(x)

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6843

x3y′′+y=1x4

["unknown"]

✗

6844

xy′′−2y′+y=cos⁡(x)

["unknown"]

✗

6845

y′−yx=cos⁡(x)

["unknown"]

✗

6846

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6847

y′′+4xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6848

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6849

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6850

y′−xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

6851

(−x2+1)y′′−y′x+p2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6852

(x2+1)y′′−2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6853

(x2+1)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6854

xy′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6855

y′′+2x3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6856

y′′−xy=11−x
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6857

x2y′′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6858

x2y′′+y′x+(x+1)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

6859

x2y′′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6860

y′′+y′x−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

6861

2xy′′+y′−x2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6862

x2y′′−y′x−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6863

x2(x2+1)y′′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6864

x2y′′+y′+y=0

["unknown"]

✗

6865

xy′′+x3y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6866

xy′′+y′x−yex=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6867

x2y′′+x2y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6868

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6869

x3y′′+(x+1)y=0

["unknown"]

✗

6870

xy′′+x5y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6871

sin⁡(x)y′′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6872

cos⁡(x)y′′−ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

6873

x2y′′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

6874

x2y′′+(x−34)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

6875

x2y′′−y′x+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7201

(x2−25)y′′+2y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7202

(x2−25)y′′+2y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7203

(x2−2x+10)y′′+y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7204

(x2−2x+10)y′′+y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7205

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7206

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7207

y′′−2y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7208

y′′−y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7209

y′′+x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7210

y′′+2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7211

(x−1)y′′+y′=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7212

(x+2)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7213

y′′−(x+1)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7214

(x2+1)y′′−6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7215

(x2+2)y′′+3y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7216

(x2−1)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7217

(x−1)y′′−y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7218

(x+1)y′′−(2−x)y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7219

y′′−2y′x+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7220

(x2+1)y′′+2y′x=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7221

y′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7222

y′′+exy′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7223

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7224

x3y′′+4x2y′+3y=0

["unknown"]

✗

7225

x(3+x)2y′′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7226

(x2−9)2y′′+(3+x)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7227

y′′−y′x+y(x−1)3=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7228

(x3+4x)y′′−2y′x+6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7229

x2(x−5)2y′′+4y′x+(x2−25)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7230

(x2+x−6)y′′+(3+x)y′+(x−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7231

x(x2+1)2y′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7232

x3(x2−25)(x−2)2y′′+3x(x−2)y′+7(5+x)y=0

["unknown"]

✗

7233

(x3−2x2+3x)2y′′+x(x−3)2y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7234

(x2−1)y′′+5(x+1)y′+(x2−x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7235

xy′′+(3+x)y′+7x2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7236

x2y′′+(53x+x2)y′−y3=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7237

xy′′+y′+10y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7238

2xy′′−y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7239

2xy′′+5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7240

4xy′′+y′2+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7241

2x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7242

3xy′′+(2−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7243

x2y′′−(x−29)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7244

2xy′′−(2x+3)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7245

x2y′′+y′x+(x2−49)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7246

9x2y′′+9x2y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7247

2x2y′′+3y′x+(2x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7248

xy′′+2y′−xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7249

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7250

xy′′−y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7251

y′′+3y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7252

xy′′+(1−x)y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7253

xy′′+y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7254

xy′′+(x−6)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7255

x(x−1)y′′+3y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7256

x4y′′+λy=0

["unknown"]

✗

7257

x3y′′+y=0

["unknown"]

✗

7258

x2y′′+(3x−1)y′+y=0

["unknown"]

✗

7259

x2y′′+y′x+(x2−19)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7260

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7261

4x2y′′+4y′x+(4x2−25)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7262

16x2y′′+16y′x+(16x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7263

xy′′+y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7264

xy′′+y′+(x−4x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7265

x2y′′+y′x+(9x2−4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7266

x2y′′+y′x+(36x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7267

x2y′′+y′x+(25x2−49)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7268

x2y′′+y′x+(2x2−64)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7269

xy′′+2y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7270

xy′′+3y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7271

xy′′−y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7272

xy′′−5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7273

x2y′′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7274

4x2y′′+(16x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7275

xy′′+3y′+x3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7276

9x2y′′+9y′x+(x6−36)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7277

y′′−x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7278

xy′′+y′−7x3y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7279

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7280

x2y′′+4y′x+(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7281

16x2y′′+32y′x+(x4−12)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7282

4x2y′′−4y′x+(16x4+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7283

2xy′′+y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7284

y′′−y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7285

(x−1)y′′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7286

y′′−x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7287

xy′′−(x+2)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7288

cos⁡(x)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7289

y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7290

(x+2)y′′+3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7291

(x+1)y′=y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

7292

y′=−2xy

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

7293

y′x−3y=k

["first_order_ode_series_frobenius"]

✓

7294

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7295

y′′−y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7296

y′′−y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7297

(−x2+1)y′′−2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7298

y′′+(x2+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7299

y′′−4y′x+(4x2−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7300

y′+4y=1
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

7301

y′′+3y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7302

(−x2+1)y′′−2y′x+30y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7303

(x−2)y′=xy
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

7304

(x−2)2y′′+(x+2)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7305

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7306

xy′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7307

xy′′+(2x+1)y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7308

xy′′+2x3y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7309

y′′+(x−1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7310

xy′′+y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7311

2x(x−1)y′′−(x+1)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7312

xy′′+2y′+4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7313

xy′′+(2−2x)y′+(x−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7314

x2y′′+6y′x+(4x2+6)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7315

xy′′+(−2x+1)y′+(x−1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7316

2x(1−x)y′′−(1+6x)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7317

x(1−x)y′′+(12+2x)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7318

4xy′′+y′+8y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7319

4(t2−3t+2)y′′−2y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7320

2(t2−5t+6)y′′+(2t−3)y′−8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7321

3t(1+t)y′′+y′t−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7322

x2y′′+y′x+(x2−449)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7323

xy′′+y′+y4=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7324

y′′+(e−2x−19)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7325

x2y′′+(x+34)y4=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7326

x2y′′+y′x+(x2−1)y4=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7327

(2x+1)2y′′+2(2x+1)y′+16xy(x+1)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7328

x2y′′+y′x+(x2−6)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7329

xy′′+5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7330

9x2y′′+9y′x+(36x4−16)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7331

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7332

4xy′′+4y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7333

xy′′+y′+36y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7334

y′′+k2x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7335

y′′+k2x4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7336

xy′′−5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7337

y′′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7338

xy′′+(−2x+1)y′+(x−1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7339

(x−1)2y′′−(x−1)y′−35y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7340

16(x+1)2y′′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7341

x2y′′+y′x+(x2−5)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7342

x2y′′+2x3y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7343

xy′′−(x+1)y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7344

xy′′+3y′+4x3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7345

y′′+y4x=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7346

xy′′+y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7687

y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7688

y′′+3x2y′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7689

y′′−x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7690

y′′+x3y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7691

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7692

y′′+(x−1)2y′−(x−1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7693

(x2+1)y′′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7694

y′′+yex=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7696

(−x2+1)y′′−2y′x+α(α+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

7708

x2y′′+(x2+x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7709

3x2y′′+x6y′+2xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7710

x2y′′−5y′+3x2y=0

["unknown"]

✗

7711

xy′′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7712

(−x2+1)y′′−2y′x+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7713

(x2+x−2)2y′′+3(x+2)y′+(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7714

x2y′′+y′sin⁡(x)+cos⁡(x)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

7715

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7716

4x2y′′+(4x4−5x)y′+(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7717

x2y′′+(−3x2+x)y′+yex=0

["second_order_ode_series_frobenius_complex_roots"]

✓

7718

3x2y′′+5y′x+3xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7719

x2y′′+y′x+x2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7720

x2y′′+xexy′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

7721

2x2y′′+(x2+5x)y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

7722

4x2y′′−4xexy′+3cos⁡(x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7723

x2(−x2+1)y′′+3(x2+x)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7724

x2y′′+3y′x+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

7725

x2y′′+2x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7726

x2y′′+5y′x+(−x3+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7727

x2y′′−2x(x+1)y′+2(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7728

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7729

x2y′′−2x2y′+(4x−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

7730

(−x2+1)y′′−2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8072

y′=2xy

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8074

y′+y=1

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8076

y′−y=2

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8078

y′+y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8080

y′−y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8082

y′−y=x2

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8084

y′x=y

["first_order_ode_series_frobenius"]

✓

8086

x2y′=y

["unknown"]

✗

8088

y′−yx=x2

["first_order_ode_series_frobenius"]

✓

8091

y′=1−x2+1

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8092

y′=1+y

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8093

y′=x−y
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8095

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8096

y′′−y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8097

y′′+2y′x−y=x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8098

y′′+y′−x2y=1

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8099

(x2+1)y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8100

y′′+(x+1)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8101

(x2+1)y′′+2y′x−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8102

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8103

y′′+y′−xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8104

y′′+y′−xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8105

y′′+(p+12−x24)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8106

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8107

(−x2+1)y′′−y′x+p2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8108

y′′−2y′x+2py=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8109

x3(x−1)y′′−2(x−1)y′+3xy=0

["unknown"]

✗

8110

x2(x2−1)y′′−x(1−x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8111

x2y′′+(2−x)y′=0

["unknown"]

✗

8112

(3x+1)xy′′−(x+1)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8113

y′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8114

xy′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8115

x2y′′+ysin⁡(x)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8116

x3y′′+ysin⁡(x)=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8117

x4y′′+ysin⁡(x)=0

["unknown"]

✗

8118

x3y′′+(cos⁡(2x)−1)y′+2xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8119

4x2y′′+(2x4−5x)y′+(3x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8120

x2y′′+3y′x+4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8121

x3y′′−4x2y′+3xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8122

4xy′′+3y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8123

2xy′′+(3−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8124

2xy′′+(x+1)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8125

2x2y′′+y′x−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8126

x2y′′+y′x+x2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8127

y′′+y′x2−yx3=0

["unknown"]

✗

8128

x2y′′+(3x−1)y′+y=0

["unknown"]

✗

8129

x2y′′−3y′x+(4x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8130

4x2y′′−8x2y′+(4x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8131

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8132

x2y′′−x2y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8133

xy′′−y′+4x3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8134

(x−1)2y′′−3(x−1)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8135

3(x+1)2y′′−(x+1)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8136

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8137

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8138

x(1−x)y′′+(32−2x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8139

(2x2+2x)y′′+(1+5x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8140

(x2−1)y′′+(5x+4)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8141

(x2−x−6)y′′+(3x+5)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8142

(−x2+1)y′′−y′x+p2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8143

(1−ex)y′′+y′2+yex=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8144

y′′+2xy=x2

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8145

y′′−y′x+y=x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8146

y′′+y′+y=x3−x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8147

2y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8148

(x2+4)y′′−y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8149

(x2+1)y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8150

y′′−(x+1)y′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8151

(x−1)y′′+(x+1)y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8152

x2(x2+1)y′′−y′x+(x+2)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8153

x2y′′+y′x+(x+1)y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8154

xy′′−4y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8155

4x2y′′+4x2y′+2y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8156

2xy′′+(1−x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8157

xy′′−(x−1)y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8158

x2y′′+x(1−x)y′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8159

xy′′+(x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8160

x3y′′′+2x2y′′+(x2+x)y′+xy=0

["unknown"]

✗

8161

x3y′′′+x2y′′−3y′x+(x−1)y=0

["unknown"]

✗

8162

x3y′′′−2x2y′′+(x2+2x)y′−xy=0

["unknown"]

✗

8163

x3y′′′+(2x3−x2)y′′−y′x+y=0

["unknown"]

✗

8164

x3y′′+x2y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8165

9(x−2)2(x−3)y′′+6x(x−2)y′+16y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8166

(−x2+1)y′′−2y′x+p(p+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8212

y′=−x+y2
i.c.

["first_order_ode_series_taylor"]

✓

8214

y′−2y=x2
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

8216

y′=y+xey
i.c.

["first_order_ode_series_taylor"]

✓

8218

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8220

y′′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8222

y′′−y′=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8224

y′′+2y′=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8226

y′′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8227

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8228

y′′−2y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8229

y′′−y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8230

y′′+x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8231

y′′+2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8232

(x−1)y′′+y′=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8233

(x+2)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8234

y′′−(x+1)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8235

(x2+1)y′′−6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8236

(x2+2)y′′+3y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8237

(x2−1)y′′+y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8238

(x−1)y′′−y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8239

(x+1)y′′−(2−x)y′+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8240

y′′−2y′x+8y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8241

(x2+1)y′′+2y′x=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8242

y′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8243

y′′+exy′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8244

cos⁡(x)y′′+y′+5y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8245

cos⁡(x)y′′+y′+5y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8246

y′′−xy=1

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8247

y′′−4y′x−4y=ex

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8248

xy′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8249

y′′+5y′x+yx=0

["unknown"]

✗

8250

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8251

y′′+cos⁡(x)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8252

x3y′′+4x2y′+3y=0

["unknown"]

✗

8253

x(3+x)2y′′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8254

(x2−9)2y′′+(3+x)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8255

y′′−y′x+y(x−1)3=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8256

(x3+4x)y′′−2y′x+6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8257

x2(x−5)2y′′+4y′x+(x2−25)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8258

(x2+x−6)y′′+(3+x)y′+(x−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8259

x(x2+1)2y′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8260

x3(x2−25)(x−2)2y′′+3x(x−2)y′+7(5+x)y=0

["unknown"]

✗

8261

(x3−2x2+3x)2y′′+x(x−3)2y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8262

(x2−1)y′′+5(x+1)y′+(x2−x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8263

xy′′+(3+x)y′+7x2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8264

x2y′′+(53x+x2)y′−y3=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8265

xy′′+y′+10y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8266

2xy′′−y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8267

2xy′′+5y′+xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8268

4xy′′+y′2+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8269

2x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8270

3xy′′+(2−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8271

x2y′′−(x−29)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8272

2xy′′−(2x+3)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8273

x2y′′+y′x+(x2−49)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8274

9x2y′′+9x2y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8275

2x2y′′+3y′x+(2x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8276

xy′′+2y′−xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8277

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8278

xy′′−y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8279

y′′+3y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8280

xy′′+(1−x)y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8281

xy′′+y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8282

xy′′+(x−6)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8283

x(x−1)y′′+3y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8284

y′′+2y′t+λy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8285

x3y′′+y=0

["unknown"]

✗

8286

x2y′′+(3x−1)y′+y=0

["unknown"]

✗

8311

2xy′′+y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8312

y′′−y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8313

(x−1)y′′+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8314

y′′−x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8315

xy′′−(x+2)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8316

cos⁡(x)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8317

y′′+y′x+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8318

(x+2)y′′+3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8319

(1−2sin⁡(x))y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8320

y′′+y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8321

xy′′+(1−cos⁡(x))y′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8322

(ex−1−x)y′′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8323

y′′+x2y′+2xy=10x3−2x+5

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8557

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8558

y′′−9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8559

y′′+3y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8560

(4x2+1)y′′−8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8561

(−4x2+1)y′′+8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8562

(x2+1)y′′−4y′x+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8563

(x2+1)y′′+10y′x+20y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8564

(x2+4)y′′+2y′x−12y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8565

(x2−9)y′′+3y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8566

y′′+2y′x+5y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8567

(x2+4)y′′+6y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8568

(2x2+1)y′′−5y′x+3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8569

y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8570

(−4x2+1)y′′+6y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8571

(2x2+1)y′′+3y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8573

y′′+y′x+3y=x2

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8574

y′′+2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8575

y′′+3y′x+7y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8576

2y′′+9y′x−36y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8577

(x2+4)y′′+y′x−9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8578

(x2+4)y′′+3y′x−8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8579

(9x2+1)y′′−18y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8580

(3x2+1)y′′+13y′x+7y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8581

(2x2+1)y′′+11y′x+9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8582

y′′−2(3+x)y′−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8583

y′′+(x−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8584

(x2−2x+2)y′′−4(x−1)y′+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8585

2x(x+1)y′′+3(x+1)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8586

4x2y′′+4y′x+(4x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8587

4x2y′′+4y′x−(4x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8588

4xy′′+3y′+3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8589

2x2(1−x)y′′−x(1+7x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8590

2xy′′+5(−2x+1)y′−5y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8591

8x2y′′+10y′x−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8592

2xy′′+(2−x)y′−2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8593

2x(3+x)y′′−3(x+1)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8594

2xy′′+(−2x2+1)y′−4xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8595

x(4−x)y′′+(2−x)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8596

3x2y′′+y′x−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8597

2xy′′+(2x+1)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8598

2xy′′+(2x+1)y′−5y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8599

2x2y′′−3x(1−x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8600

2x2y′′+x(4x−1)y′+2(3x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8601

2xy′′−(2x2+1)y′−xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8602

2x2y′′+y′x−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8603

2x2y′′−3y′x+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8604

9x2y′′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8605

2x2y′′+5y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8616

x2y′′−x(x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8617

4x2y′′+(−2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8618

x2y′′+x(x−3)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8619

x2y′′+3y′x+(4x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8620

x(x+1)y′′+(1+5x)y′+3y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8621

x2y′′−x(3x+1)y′+(1−6x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8622

x2y′′+x(x−1)y′+(1−x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8623

x(x−2)y′′+2(x−1)y′−2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8624

x(x−2)y′′+2(x−1)y′−2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8625

4(x−4)2y′′+(x−4)(x−8)y′+xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8627

xy′′+y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8628

xy′′+(−x2+1)y′−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8629

x2y′′+x(2x+3)y′+(3x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8630

4x2y′′+8x(x+1)y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8631

x2y′′+3x(x+1)y′+(1−3x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8632

xy′′+(1−x)y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8633

x2y′′+2x(x−2)y′+2(2−3x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8634

x2(2x+1)y′′+2x(1+6x)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8635

x2y′′+x(3x+2)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8636

xy′′−(3+x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8637

x(x+1)y′′+(5+x)y′−4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8638

x(x+1)y′′+(5+x)y′−4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8639

x2y′′+x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8640

x(1−x)y′′−3y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8641

x(1−x)y′′−3y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8642

xy′′+(3x+4)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8643

xy′′−2(x+2)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8644

xy′′+(2x+3)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8645

x(3+x)y′′−9y′−6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8646

x(−2x+1)y′′−2(x+2)y′+8y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8647

xy′′+(x3−1)y′+x2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8648

x2(4x−1)y′′+x(1+5x)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8649

xy′′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8650

x2y′′−3y′x+(4x+3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8651

2xy′′+6y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8652

4x2y′′+2x(2−x)y′−(3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8653

x2y′′−x(6+x)y′+10y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8654

xy′′+(2x+3)y′+8y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8655

x(1−x)y′′+2(1−x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8656

x(1−x)y′′+2(1−x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8658

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8659

x2y′′−5y′x+(8+5x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8660

xy′′+(3−x)y′−5y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8661

9x2y′′−15y′x+7(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8662

x2y′′+x(−2x+1)y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8663

x2y′′+3y′x+(x3+x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8664

2x(1−x)y′′+(−2x+1)y′+(x+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8665

xy′′+y′+xy(x+1)=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8666

x2y′′+x(x+1)y′−(6x2−3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8667

xy′′+y′x+(x4+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8668

x(x−2)2y′′−2(x−2)y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8669

x(x−2)2y′′−2(x−2)y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8670

2xy′′+(1−x)y′−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8671

xy′′−(x+2)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8672

xy′′−(x+2)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8673

x2y′′+2x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8674

2x2y′′−x(2x+7)y′+2(5+x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8675

x2(x2+1)y′′+2x(x2+3)y′+6y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8676

(−x2+1)y′′−10y′x−18y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8677

2xy′′+(2x+1)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8678

y′′+2y′x−8y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8679

x(−x2+1)y′′−(x2+7)y′+4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8680

2x2y′′−x(2x+1)y′+(1+4x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8681

4x2y′′−2x(x+2)y′+(3+x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8682

x2y′′−x(x2+1)y′+(−x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8683

2xy′′+y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8684

x2y′′+x(x2−3)y′+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8685

4x2y′′−x2y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8686

(x2+1)y′′−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8687

2x2y′′−x(2x+1)y′+(3x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8688

4x2y′′+3x2y′+(3x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8689

xy′′+(−x2+1)y′+2xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8690

4x2y′′+2x2y′−(3+x)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8691

x(−x2+1)y′′+5(−x2+1)y′−4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8692

x2y′′+(3+x)xy′+(2x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8693

x2y′′+y′x−(x2+4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8694

x(−2x+1)y′′−2(x+2)y′+18y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8695

xy′′+(2−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8696

x2y′′−3y′x+4(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8890

2x2y′′−y′x+(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8891

2x2y′′−y′x+(−x2+1)y=1

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8892

2x2y′′−y′x+(−x2+1)y=x+1

["unknown"]

✗

8893

2x2y′′−y′x+(−x2+1)y=x

["unknown"]

✗

8894

2x2y′′−y′x+(−x2+1)y=x2+x+1

["unknown"]

✗

8895

2x2y′′−y′x+(−x2+1)y=x2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8896

2x2y′′−y′x+(−x2+1)y=x2+1

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8897

2x2y′′−y′x+(−x2+1)y=x4

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8898

2x2y′′−y′x+(−x2+1)y=sin⁡(x)

["unknown"]

✗

8899

2x2y′′−y′x+(−x2+1)y=1+sin⁡(x)

["unknown"]

✗

8900

2x2y′′−y′x+(−x2+1)y=xsin⁡(x)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8901

2x2y′′−y′x+(−x2+1)y=cos⁡(x)+sin⁡(x)

["unknown"]

✗

8902

x2y′′+(cos⁡(x)−1)y′+yex=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8903

(x−2)y′′+y′x+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8904

(x−2)y′′+y′x+(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8905

(x+1)(3x−1)y′′+cos⁡(x)y′−3xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8906

xy′′+2y′+xy=0
i.c.

["unknown"]

✗

8907

2x2y′′+3y′x−xy=x2+2x

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8908

2x2y′′−y′x+(−x2+1)y=1

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8909

2x2y′′+2y′x−xy=1

["unknown"]

✗

8910

y′′+(x−6)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8911

x2y′′+(3x2+2x)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8912

2x2y′′−y′x+(−x2+1)y=x2+cos⁡(x)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8913

2x2y′′−y′x+(−x2+1)y=cos⁡(x)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8914

2x2y′′−y′x+(−x2+1)y=x3+cos⁡(x)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8915

2x2y′′−y′x+(−x2+1)y=x3cos⁡(x)

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8916

2x2y′′−y′x+(−x2+1)y=x3cos⁡(x)+sin⁡(x)2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8917

2x2y′′−y′x+(−x2+1)y=ln⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8918

2x2(x2+x+1)y′′+x(11x2+11x+9)y′+(7x2+10x+6)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8919

(3+x)x2y′′+5x(x+1)y′−(1−4x)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8920

x2(−x2+2)y′′−x(4x2+3)y′+(−2x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8923

x2y′′+y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8924

xy′′+y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8925

4xy′′+2y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8926

xy′′+y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8927

xy′′+(x+1)y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8928

x(x−1)y′′+3y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8929

x2(x2−2x+1)y′′−(3+x)xy′+(x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8930

2x2(x+2)y′′+5x2y′+(x+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8931

2x2y′′+y′x+(x−5)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8932

2x2y′′+2y′x−xy=sin⁡(x)

["second_order_ode_series_frobenius_repeated_roots"]

✓

8933

2x2y′′+2y′x−xy=xsin⁡(x)

["second_order_ode_series_frobenius_repeated_roots"]

✓

8934

2x2y′′+2y′x−xy=sin⁡(x)cos⁡(x)

["second_order_ode_series_frobenius_repeated_roots"]

✓

8935

2x2y′′+2y′x−xy=x3+xsin⁡(x)

["second_order_ode_series_frobenius_repeated_roots"]

✓

8936

cos⁡(x)y′′+2y′x−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8937

x2y′′+4y′x+(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8938

x2y′′+y′x−xy=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8939

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8940

(x2−x)y′′−y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8941

x2y′′+(x2+6x)y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8942

x2y′′−y′x+(x2−8)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8943

x2y′′−9y′x+25y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

8944

x2y′′−y′x−(x2+54)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8945

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8946

xy′′+(2−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8947

2x2y′′+3y′x−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

8948

2x2y′′+5y′x+4y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

8949

x2y′′+3y′x+4yx4=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8950

x2y′′−xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

8951

(−x2+1)y′′+y′+y=xex

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8958

y′′+(x−1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

8968

y′+y=1x

["unknown"]

✗

8969

y′+y=1x2

["unknown"]

✗

8970

y′x+y=0

["first_order_ode_series_frobenius"]

✓

8971

y′=1x

["unknown"]

✗

8972

y′′=1x

["unknown"]

✗

8973

y′′+y′=1x

["unknown"]

✗

8974

y′′+y=1x

["unknown"]

✗

8975

y′′+y′+y=1x

["unknown"]

✗

8979

y′′+y=eacos⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

9166

x2y′′−x(6+x)y′+10y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

9167

x2y′′+y′x+(x2−5)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13489

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13490

y′′+8y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13491

y′′+y′x+(2x2+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13492

y′′+y′x+(x2−4)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13493

y′′+y′x+(3x+2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13494

y′′−y′x+(3x−2)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13495

(x2+1)y′′+y′x+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13496

(x−1)y′′−(3x−2)y′+2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13497

(x3−1)y′′+x2y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13498

(3+x)y′′+(x+2)y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13499

y′′−y′x−y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13500

y′′+y′x−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13501

(x2+1)y′′+y′x+2xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13502

(2x2−3)y′′−2y′x+y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13503

x2y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13504

x2y′′+3y′x−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13505

xy′′+y′+2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13506

(−x2+1)y′′−2y′x+n(n+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13507

(x2−3x)y′′+(x+2)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13508

(x3+x2)y′′+(x2−2x)y′+4y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

13509

(x4−2x3+x2)y′′+2(x−1)y′+x2y=0

["unknown"]

✗

13510

(x5+x4−6x3)y′′+x2y′+(x−2)y=0

["unknown"]

✗

13511

2x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13512

2x2y′′+y′x+(2x2−3)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13513

x2y′′−y′x+(x2+89)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13514

x2y′′−y′x+(2x2+59)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13515

x2y′′+y′x+(x2−19)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13516

2xy′′+y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13517

3xy′′−(x−2)y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13518

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13519

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13520

x2y′′+(x4+x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13521

xy′′−(x2+2)y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13522

x2y′′+x2y′−2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13523

(2x2−x)y′′+(2x−2)y′+(−2x2+3x−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13524

x2y′′−y′x+3y4=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13525

x2y′′+y′x+(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13526

x2y′′+(x3−x)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13527

x2y′′−y′x+8(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13528

x2y′′+x2y′−3y4=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13529

xy′′+y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

13530

2xy′′+6y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13531

x2y′′−y′x+(x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

13532

x2y′′−y′x+(x2−3)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13736

(−x2+1)y′′−2y′x+n(n+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13737

y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13738

(x2+1)y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13739

2xy′′+y′−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13740

y′′−2y′x−4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13741

y′′−2y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

13742

x(1−x)y′′−3y′x−y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13743

x2y′′+y′x−x2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

13744

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

13745

x2y′′+y′x+(−n2+x2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

13843

y′′+4xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

14067

x(1−x)y′′+(1−5x)y′−4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

14068

(x2−1)2y′′+(x+1)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

14069

xy′′+4y′−xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

14070

2xy′′+(x+1)y′−ky=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

14071

x3y′′+x2y′+y=0

["unknown"]

✗

14072

x2y′′+y′−2y=0

["unknown"]

✗

14073

2x2y′′+x(1−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

14074

x(x−1)y′′+3y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15576

y′−2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15577

y′−2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15578

y′+2y2x−1=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15579

(x−3)y′−2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15580

(x2+1)y′−2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15581

y′+yx−1=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15582

y′+yx−1=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15583

(1−x)y′−2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15584

(−x3+2)y′−3x2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15585

(−x3+2)y′+3x2y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15586

(x+1)y′−xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15587

(x+1)y′+(1−x)y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15588

(x2+1)y′′−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15589

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15590

(x2+4)y′′+2y′x=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15591

y′′−3x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15592

(−x2+4)y′′−5y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15593

(−x2+1)y′′−y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15594

y′′−2y′x+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15595

(x2−6x)y′′+4(x−3)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15596

y′′+(x+2)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15597

(x2−2x+2)y′′+(1−x)y′−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15598

y′′−2y′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15599

y′′−y′x−2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15600

(−x2+1)y′′−y′x+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15601

(−x2+1)y′′−2y′x+λy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15602

y′′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15603

y′′−x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15604

y′′+e2xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15605

sin⁡(x)y′′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15606

y′′+xy=sin⁡(x)

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15607

y′′−y′sin⁡(x)−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15608

y′′−y2=0

["second_order_ode_series_taylor"]

✓

15609

y′+cos⁡(y)=0

["first_order_ode_series_taylor"]

✓

15610

y′−yex=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15611

y′−ytan⁡(x)=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15612

sin⁡(x)y′′+x2y′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15613

sinh⁡(x)y′′+x2y′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15614

sinh⁡(x)y′′+x2y′−ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15615

e3xy′′+y′sin⁡(x)+2yx2+4=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15616

y′′+(ex+1)y1−ex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15617

(x2−4)y′′+(x2+x−6)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15618

xy′′+(1−ex)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15619

sin⁡(πx2)y′′+x2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15620

y′−yex=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15621

y′+e2xy=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15622

y′+cos⁡(x)y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15623

y′+yln⁡(x)=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15624

y′′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15625

y′′+3y′x−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15626

xy′′−3y′x+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15627

y′′+yln⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15628

xy′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15629

y′′+(6x2+2x+1)y′+(2+12x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15630

y′−yex=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15631

y′+x2+1y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15632

cos⁡(x)y′+y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15633

y′+2x2+1y=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

15634

y′′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15635

y′′+cos⁡(x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15636

y′′+y′sin⁡(x)+cos⁡(x)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15637

xy′′+y′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15638

(x−3)2y′′−2(x−3)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15639

2x2y′′+5y′x+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15640

(x−1)2y′′−5(x−1)y′+9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15641

(x+2)2y′′+(x+2)y′=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15642

3(x−2)2y′′−4(x−5)y′+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15643

(x−5)2y′′+(x−5)y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15644

x2y′′+xy′x−2+2yx+2=0

["second_order_ode_series_frobenius_complex_roots"]

✓

15645

x3y′′+x2y′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15646

(−x4+x3)y′′+(3x−1)y′+827y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15647

y′′+y′x−3+yx−4=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15648

y′′+y′(x−3)2+y(x−4)2=0

["second_order_ode_series_frobenius_complex_roots"]

✓

15649

y′′+(1x−13)y′+(1x−14)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15650

(4x2−1)y′′+(4−2x)y′+(−x2+1)yx2+1=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15651

(x2+4)2y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

15652

x2y′′−2y′x+(x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15653

4x2y′′+(1−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15654

x2y′′+y′x+(4x−4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15655

(−9x4+x2)y′′−6y′x+10y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15656

x2y′′−y′x+y1−x=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15657

y′′+y′x+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15658

y′′+y′x+(1−1x2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15659

2x2y′′+(−2x3+5x)y′+(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15660

x2y′′−(2x2+5x)y′+(9+4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15661

(−3x3+3x2)y′′−(5x2+4x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15662

x2y′′−(x2+x)y′+4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15663

4x2y′′+8x2y′+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15664

x2y′′+(−x4+x)y′+3x3y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15665

(9x3+9x2)y′′+(27x2+9x)y′+(8x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15666

(x−3)y′′+(x−3)y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15667

y′′+2y′x+2+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15668

4y′′+(4x−3)y(x−1)2=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15669

(x−3)2y′′+(x2−3x)y′−3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15670

x2y′′−2y′x+(−x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15671

x2y′′−2x2y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15672

y′′+y′x+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15673

x2(−x2+2)y′′+(4x2+5x)y′+(x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15674

x2y′′−(2x2+5x)y′+9y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15675

x2(2x+1)y′′+y′x+(4x3−4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15676

4x2y′′+8y′x+(1−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15677

x2y′′+y′x−(2x+1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15678

xy′′+4y′+12y(x+2)2=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15679

xy′′+4y′+12y(x+2)2=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15680

(x−3)y′′+(x−3)y′+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15681

(−x2+1)y′′−y′x+3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

15682

4x2y′′+(1−4x)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15683

y′′+y′x+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

15684

x2y′′−(x2+x)y′+4xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

15685

x2y′′+y′x+(4x−4)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16436

x2y′′−2y′x+7y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16437

(x−2)y′′+y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16438

(x2−4)y′′+16(x+2)y′−y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16439

y′′+3y′−18y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16440

y′′−11y′+30y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16441

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16442

y′′−y′−2y=e−x

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16443

(−2−2x)y′′+2y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16444

(3x+2)y′′+3y′x=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16445

(3x+1)y′′−3y′−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16446

(−x2+2)y′′+2(x−1)y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16447

y′′−y′x+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16448

(2x2+2)y′′+2y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16449

(3−2x)y′′+2y′−2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16450

y′′−4x2y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16451

(2x2−1)y′′+2y′x−3y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16452

y′′+y′x=sin⁡(x)
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16453

y′′+y′+xy=cos⁡(x)
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16454

y′′+(−1+y2)y′+y=0
i.c.

["second_order_ode_series_taylor"]

✓

16455

y′′+(y′23−1)y′+y=0
i.c.

["second_order_ode_series_taylor"]

✓

16456

y′′−2y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16457

y′′−2y′x+6y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16458

(−x2+1)y′′−y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16459

(−x2+1)y′′−y′x+9y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16460

y′′−cos⁡(x)y=sin⁡(x)
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16461

x2y′′+6y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

16462

x(x+1)y′′+y′x2+5y=0

["unknown"]

✗

16463

(x2−3x−4)y′′−(x+1)y′+(x2−1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16464

(x2−25)2y′′−(5+x)y′+10y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16465

2xy′′−5y′−3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16466

5xy′′+8y′−xy=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16467

9xy′′+14y′+(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16468

7xy′′+10y′+(−x2+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16469

x2y′′+y′x+(x−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16470

xy′′+2y′x+y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16471

y′′+8y′3x−(23x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16472

y′′+(163x−1)y′−16y3x2=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16473

y′′+(12x−2)y′−35y16x2=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16474

y′′−(1x+2)y′+(x+1x2)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16475

x2y′′+7y′x−7y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16476

x2y′′+3y′x+y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16477

x2y′′−3y′x+4y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16478

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16479

x2y′′+y′x+(−k2+x2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16480

(−x2+1)y′′−2y′x+k(k+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16481

x(1−x)y′′+(12−3x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16482

x(1−x)y′′+y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16483

x(1−x)y′′+(−2x+1)y′+2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16484

xy′′+(1−x)y′+ky=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16485

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16486

x2y′′+y′x+(16x2−25)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16543

y′′−4y′+4y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16544

y′′+2y′−3y=xex

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16545

(2x2−1)y′′+2y′x−3y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

16546

3xy′′+11y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16547

2x2y′′+5y′x−2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

16548

x2y′′−7y′x+(−2x2+7)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

16549

x(1−x)y′′+(2x+1)y′+10y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

16550

x(x+1)y′′+(−2x+1)y′−10y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

17127

y′=1−xy
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

17128

y′=y−xx+y
i.c.

["first_order_ode_series_taylor"]

✓

17129

y′=ysin⁡(x)
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

17130

y′′+xy=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17131

y′′−y′sin⁡(x)=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17132

xy′′+ysin⁡(x)=x
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17133

ln⁡(x)y′′−ysin⁡(x)=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17134

y′′′+xsin⁡(y)=0
i.c.

["unknown"]

✗

17135

y′−2xy=0
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

17136

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17137

y′′−y′x+y=1
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17138

y′′−(x2+1)y=0
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17139

y′′=x2y−y′
i.c.

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17140

y′′−yex=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

17141

y′=ey+xy
i.c.

["first_order_ode_series_taylor"]

✓

17142

4xy′′+2y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

17143

(x+1)y′−ny=0

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

17144

9x(1−x)y′′−12y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18336

y′=2xy

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

18337

y′+y=1

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

18338

y′x=y

["first_order_ode_series_frobenius"]

✓

18339

x2y′=y

["unknown"]

✗

18340

y′=1+y2
i.c.

["first_order_ode_series_taylor"]

✓

18341

y′=x−y
i.c.

["first_order_ode_series_taylor", "first_order_ode_series_ordinary"]

✓

18342

(x2+1)y′′+2y′x−2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18344

y′′+y′x+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18345

y′′+y′−xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18346

y′′+xy=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18347

(−x2+1)y′′−y′x+n2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18348

y′′−2y′x+2ny=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18349

x3(x−1)y′′−2(x−1)y′+3xy=0

["unknown"]

✗

18350

x2(x2−1)2y′′−x(1−x)y′+2y=0

["second_order_ode_series_frobenius_complex_roots"]

✓

18351

x2y′′+(2−x)y′=0

["unknown"]

✗

18352

(3x+1)xy′′−(x+1)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18353

y′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18354

xy′′+ysin⁡(x)=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18355

x2y′′+ysin⁡(x)=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18356

x3y′′+ysin⁡(x)=0

["second_order_ode_series_frobenius_complex_roots"]

✓

18357

x4y′′+ysin⁡(x)=0

["unknown"]

✗

18358

x3y′′+(cos⁡(2x)−1)y′+2xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18359

4x2y′′+(2x4−5x)y′+(3x2+2)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18360

4xy′′+2y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18361

2xy′′+(3−x)y′−y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18362

2xy′′+(x+1)y′+3y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18363

2x2y′′+y′x−(x+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18364

x2y′′+y′x+x2y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

18365

y′′+y′x2−yx3=0

["unknown"]

✗

18366

y′′+ny′x2+qyx3=0

["unknown"]

✗

18367

x2y′′−3y′x+(4x+4)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

18368

4x2y′′−8x2y′+(4x2+1)y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

18369

xy′′+2y′+xy=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18370

x2y′′−x2y′+(x2−2)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18371

xy′′−y′+4x3y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18372

x2y′′+y′x+(x2−1)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18373

x2y′′+y′x+(x2−14)y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18374

x(1−x)y′′+(32−2x)y′+2y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18375

(2x2+2x)y′′+(1+5x)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18376

(x2−1)y′′+(5x+4)y′+4y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18377

(x2−x−6)y′′+(3x+5)y′+y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18378

x(1−x)y′′+(1−3x)y′−y=0

["second_order_ode_series_frobenius_repeated_roots"]

✓

18379

(−x2+1)y′′−2y′x+n(n+1)y=0

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18380

x2y′′+y′x+(−n2+x2)y=0

["unknown"]

✗

18905

(−x2+x)y′′+4y′+2y=0

["second_order_ode_series_frobenius_roots_difference_is_integer"]

✓

18906

x4y′′+y′x+y=1x

["unknown"]

✗

18907

y′′+y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18908

(2x2+1)y′′+y′x+2y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

18909

2x2y′′−y′x+(−x2+1)y=x2

["second_order_ode_series_frobenius_roots_difference_not_integer"]

✓

18910

(−x2+1)y′′−2y′x+n(n+1)y=0

["second_order_ode_series_taylor", "second_order_ode_series_ordinary"]

✓

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