6.5 Problems 401 to 500

Table 6.9: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

401

\[ {}y^{\prime } = 4 y \]

402

\[ {}2 y^{\prime }+3 y = 0 \]

403

\[ {}y^{\prime }+2 x y = 0 \]

404

\[ {}y^{\prime } = x y \]

405

\[ {}\left (x -2\right ) y^{\prime }+y = 0 \]

406

\[ {}\left (2 x -1\right ) y^{\prime }+2 y = 0 \]

407

\[ {}2 \left (1+x \right ) y^{\prime }+y = 0 \]

408

\[ {}\left (x -1\right ) y^{\prime }+2 y = 0 \]

409

\[ {}2 \left (x -1\right ) y^{\prime } = 3 y \]

410

\[ {}y^{\prime \prime } = y \]

411

\[ {}y^{\prime \prime } = 4 y \]

412

\[ {}y^{\prime \prime }+9 y = 0 \]

413

\[ {}y^{\prime \prime }+y = x \]

414

\[ {}x y^{\prime }+y = 0 \]

415

\[ {}2 x y^{\prime } = y \]

416

\[ {}x^{2} y^{\prime }+y = 0 \]

417

\[ {}x^{3} y^{\prime } = 2 y \]

418

\[ {}y^{\prime \prime }+4 y = 0 \]

419

\[ {}y^{\prime \prime }-4 y = 0 \]

420

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

421

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]

422

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \]

423

\[ {}y^{\prime \prime } = y^{\prime }+y \]

424

\[ {}y^{\prime } = 1+y^{2} \]

425

\[ {}y^{\prime \prime \prime } = y \]

426

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

427

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

428

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

429

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

430

\[ {}\left (x^{2}-3\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

431

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

432

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

433

\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \]

434

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

435

\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

436

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

437

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

438

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]

439

\[ {}y^{\prime \prime }+x y = 0 \]

440

\[ {}y^{\prime \prime }+x^{2} y = 0 \]

441

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

442

\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

443

\[ {}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0 \]

444

\[ {}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0 \]

445

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

446

\[ {}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \]

447

\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]

448

\[ {}y^{\prime \prime }+\left (1+x \right ) y = 0 \]

449

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0 \]

450

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \]

451

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0 \]

452

\[ {}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \]

453

\[ {}y^{\prime \prime }+{\mathrm e}^{-x} y = 0 \]

454

\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \]

455

\[ {}y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+x y = 0 \]

456

\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \]

457

\[ {}y^{\prime \prime } x +\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right ) = 0 \]

458

\[ {}y^{\prime \prime } x +x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y = 0 \]

459

\[ {}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+x y = 0 \]

460

\[ {}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0 \]

461

\[ {}x \left (1+x \right ) y^{\prime \prime }+2 y^{\prime }+3 x y = 0 \]

462

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

463

\[ {}x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y = 0 \]

464

\[ {}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y = 0 \]

465

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \]

466

\[ {}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0 \]

467

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

468

\[ {}\left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y = 0 \]

469

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y = 0 \]

470

\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0 \]

471

\[ {}\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0 \]

472

\[ {}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0 \]

473

\[ {}4 y^{\prime \prime } x +2 y^{\prime }+y = 0 \]

474

\[ {}2 y^{\prime \prime } x +3 y^{\prime }-y = 0 \]

475

\[ {}2 y^{\prime \prime } x -y^{\prime }-y = 0 \]

476

\[ {}3 y^{\prime \prime } x +2 y^{\prime }+2 y = 0 \]

477

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y = 0 \]

478

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y = 0 \]

479

\[ {}6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y = 0 \]

480

\[ {}3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y = 0 \]

481

\[ {}2 y^{\prime \prime } x +\left (1+x \right ) y^{\prime }+y = 0 \]

482

\[ {}2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0 \]

483

\[ {}y^{\prime \prime } x +2 y^{\prime }+9 x y = 0 \]

484

\[ {}y^{\prime \prime } x +2 y^{\prime }-4 x y = 0 \]

485

\[ {}4 y^{\prime \prime } x +8 y^{\prime }+x y = 0 \]

486

\[ {}y^{\prime \prime } x -y^{\prime }+4 x^{3} y = 0 \]

487

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y = 0 \]

488

\[ {}2 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (2 x +1\right ) y = 0 \]

489

\[ {}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (1+x \right ) y = 0 \]

490

\[ {}2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0 \]

491

\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]

492

\[ {}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0 \]

493

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

494

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \]

495

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0 \]

496

\[ {}x \left (x -1\right ) \left (1+x \right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (1+x \right ) y^{\prime }-2 \left (x -1\right ) y = 0 \]

497

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0 \]

498

\[ {}y^{\prime \prime } x +\left (3-x \right ) y^{\prime }-y = 0 \]

499

\[ {}y^{\prime \prime } x +\left (5-x \right ) y^{\prime }-y = 0 \]

500

\[ {}y^{\prime \prime } x +\left (3 x +5\right ) y^{\prime }+3 y = 0 \]