3.1.9 Problems 801 to 900

Table 3.17: First order ode

#

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

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

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

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

2314

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

2315

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

2316

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

2317

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

2318

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

2319

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

2320

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

2321

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

2322

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

2323

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

2324

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

2325

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

2326

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

2327

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

2328

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

2329

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

2330

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

2331

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

2332

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

2333

\[ {}8 x +1 = y {y^{\prime }}^{2} \]

2334

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

2335

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

2336

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

2337

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

2338

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

2339

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

2340

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

2341

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

2342

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

2343

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

2344

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

2345

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

2346

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

2347

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

2348

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

2349

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

2350

\[ {}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \]

2351

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

2352

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

2353

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

2354

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

2355

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

2356

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

2357

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

2358

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

2359

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

2360

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

2361

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

2362

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

2363

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

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

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

2443

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

2444

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

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

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