3.9.9 Problems 801 to 900

Table 3.523: First order ode linear in derivative

#

ODE

Mathematica

Maple

2063

\[ {}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \]

2064

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

2065

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

2066

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

2067

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

2068

\[ {}x y^{\prime }-5 y-x \sqrt {y} = 0 \]

2069

\[ {}x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1} = 0 \]

2070

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

2071

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

2072

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

2073

\[ {}x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \]

2074

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

2075

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

2076

\[ {}x y^{\prime }+y = x^{3} y^{6} \]

2077

\[ {}x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \]

2078

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

2079

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

2080

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

2081

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

2082

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

2083

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

2084

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

2085

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

2086

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

2087

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

2198

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

2432

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

2433

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

2434

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

2435

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

2436

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

2437

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

2438

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

2439

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

2440

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

2441

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

2442

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

2445

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

2446

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

2447

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

2448

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

2449

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

2450

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

2451

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

2452

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

2453

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

2454

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

2455

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

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

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

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

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

2473

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

2474

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

2475

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

2476

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

2477

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

2478

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

2479

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

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

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

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

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