4.5 Problems 401 to 500

Table 4.9: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

401

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

402

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

403

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

404

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

405

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

406

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

407

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

408

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

409

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

410

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

411

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

412

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

413

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

414

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

415

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

416

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

417

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

418

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

419

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

420

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

421

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

422

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

423

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

424

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

425

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

426

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

427

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

428

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

429

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

430

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

431

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

432

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

433

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

434

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

435

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

436

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

437

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

438

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

439

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

440

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

441

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

442

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

443

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

444

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

445

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

446

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

447

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

448

\[ {}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t \]

449

\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2} \]

450

\[ {}y+y^{\prime } = 1+t \,{\mathrm e}^{-t} \]

451

\[ {}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right ) \]

452

\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t} \]

453

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

454

\[ {}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}} \]

455

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

456

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

457

\[ {}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t} \]

458

\[ {}y+y^{\prime } = 5 \sin \left (2 t \right ) \]

459

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

460

\[ {}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t \]

461

\[ {}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t} \]

462

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

463

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

464

\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} \]

465

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

466

\[ {}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t} \]

467

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

468

\[ {}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \]

469

\[ {}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}} \]

470

\[ {}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \]

471

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

472

\[ {}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t} \]

473

\[ {}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t} \]

474

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

475

\[ {}\frac {2 y}{3}+y^{\prime } = -\frac {t}{2}+1 \]

476

\[ {}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right ) \]

477

\[ {}-y+y^{\prime } = 1+3 \sin \left (t \right ) \]

478

\[ {}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t \]

479

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

480

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

481

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

482

\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \]

483

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

484

\[ {}x y^{\prime } = \sqrt {1-y^{2}} \]

485

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

486

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

487

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

488

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

489

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

490

\[ {}r^{\prime } = \frac {r^{2}}{x} \]

491

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

492

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

493

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

494

\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \]

495

\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \]

496

\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \]

497

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

498

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

499

\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \]

500

\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \]