3.9.3 Problems 201 to 300

Table 3.511: First order ode linear in derivative

#

ODE

Mathematica

Maple

491

y=2xy+x2y

492

y=xy2x2+1

493

y=2x1+2y

494

y=x(x2+1)4y3

495

y=ex+3x25+2y

496

y=exex3+4y

497

sin(2x)+cos(3y)y=0

498

x2+1y2y=arcsin(x)

499

y=3x2+16y+3y2

500

y=3x24+3y2

501

y=2y2+xy2

502

y=2ex3+2y

503

y=2cos(2x)3+2y

504

y=2(1+x)(1+y2)

505

y=t(4y)y3

506

y=ty(4y)t+1

507

y=ay+bd+cy

508

y=x2+xy+y2x2

509

y=x2+3y22xy

510

y=4y3x2xy

511

y=4x+3yy+2x

512

y=3y+xxy

513

x2+3xy+y2x2y=0

514

y=x23y22xy

515

y=3y2x22xy

516

ln(t)y+(t3)y=2t

517

y+(t4)ty=0

518

tan(t)y+y=sin(t)

519

2ty+(t2+4)y=3t2

520

2ty+(t2+4)y=3t2

521

y+ln(t)y=cot(t)

522

y=t2+13yy2

523

y=cot(t)y1+y

524

y=4ty

525

y=2ty2

526

y3+y=0

527

y=t2(t3+1)y

528

y=t(3y)y

529

y=y(3ty)

530

y=y(3ty)

531

y=t1y2

532

y=ay+by2

533

y=y(2+y)(1+y)

534

y=1+ey

535

y=1+ey

536

y=2arctan(y)1+y2

537

y=k(1+y)2

538

y=y2(y21)

539

y=y(1y2)

540

y=by+ay

541

y=y2(4y2)

542

y=(1y)2y2

543

3+2x+(2+2y)y=0

544

2x+4y+(2x2y)y=0

545

2+3x22xy+(3x2+6y2)y=0

546

2y+2xy2+(2x+2x2y)y=0

547

y=axbybx+cy

548

y=ax+bybxcy

549

exsin(y)2ysin(x)+(2cos(x)+excos(y))y=0

550

exsin(y)+3y(3xexsin(y))y=0

551

2x2exysin(2x)+exycos(2x)y+(3+exyxcos(2x))y=0

552

yx+6x+(ln(x)2)y=0

553

xln(x)+xy+(yln(x)+xy)y=0

554

x(x2+y2)32+yy(x2+y2)32=0

555

2xy+(x+2y)y=0

556

1+9x2+y+(x4y)y=0

557

x2y3+x(1+y2)y=0

558

y+(2xeyy)y=0

559

(2+x)sin(y)+xcos(y)y=0

560

2xy+3x2y+y3+(x2+y2)y=0

561

y=1+e2x+y

562

1+(sin(y)+xy)y=0

563

y+(e2y+2xy)y=0

564

ex+(excot(y)+2csc(y)y)y=0

565

4x3y2+3y+(3xy2+4y)y=0

566

3x+6y+(x2y+3yx)y=0

567

3xy+y2+(xy+x2)y=0

568

y=x32yx

569

y=cos(x)+12sin(y)

570

y=y+2x3x+3y2

571

y=36x+y2xy

572

y=12xyy2x2+2xy

573

xy+xy=1y

574

y=4x3+1y(2+3y)

575

2y+xy=sin(x)x

576

y=12xyx2+2y

577

x2+x+1x2+yy2+y=0

578

x2+y+(ey+x)y=0

579

y+y=11+ex

580

y=1+2x+y2+2xy2

581

x+y+(2y+x)y=0

582

(1+ex)y=yexy

583

y=e2ycos(x)+cos(y)ex2e2ysin(x)sin(y)ex

584

y=e2x+3y

585

2y+y=ex22x

586

y=3x22yy32x+3xy2

587

y=ex+y

588

4+6xy+2y23x2+4xy+3y2+y=0

589

y=x211+y2

590

(t+1)y+ty=e2t