3.1.10 Problems 901 to 1000

Table 3.19: First order ode

#

ODE

Mathematica

Maple

2456

\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y} \]

2457

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

2458

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

2459

\[ {}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \]

2460

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

2461

\[ {}y^{\prime } = -\frac {t}{y} \]

2462

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

2463

\[ {}y^{\prime } = y-1 \]

2464

\[ {}y^{\prime } = 1-y \]

2465

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

2466

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

2467

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

2468

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

2469

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

2470

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

2471

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

2472

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

2473

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

2474

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

2475

\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3} \]

2476

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

2477

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

2478

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

2479

\[ {}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right ) \]

2480

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

2481

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

2482

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

2483

\[ {}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y \]

2484

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

2485

\[ {}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \]

2486

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

2487

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

2488

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

2489

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

2490

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

2491

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

2492

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

2493

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

2494

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

2495

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

2496

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

2497

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

2498

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

2499

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

2500

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

2501

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

2502

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

2503

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

2504

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

2505

\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \]

2506

\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \]

2507

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

2508

\[ {}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3 \]

2509

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

2510

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

2511

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

2544

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

2545

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

2546

\[ {}{\mathrm e}^{x +y} y^{\prime }-1 = 0 \]

2547

\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \]

2548

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

2549

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

2550

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

2551

\[ {}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \]

2552

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

2553

\[ {}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32 \]

2554

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

2555

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

2556

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

2557

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

2558

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

2559

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

2560

\[ {}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right ) \]

2561

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

2562

\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = 4 x \]

2563

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

2564

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

2565

\[ {}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2} \]

2566

\[ {}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3} \]

2567

\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \]

2568

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

2569

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

2570

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

2571

\[ {}y^{\prime }+\alpha y = {\mathrm e}^{\beta x} \]

2572

\[ {}y^{\prime }+\frac {m}{x} = \ln \left (x \right ) \]

2573

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

2574

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

2575

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

2576

\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

2577

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

2578

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

2579

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

2580

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

2581

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

2582

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

2583

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

2584

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

2585

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

2586

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

2590

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