4.24 Problems 2301 to 2400

Table 4.47: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

2301

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

2302

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

2303

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

2304

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

2305

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

2306

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

2307

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

2308

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

2309

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

2310

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

2311

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

2312

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

2313

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

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

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

2364

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

2365

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

2366

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

2367

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

2368

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

2369

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

2370

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

2371

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

2372

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

2373

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

2374

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

2375

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

2376

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

2377

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

2378

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

2379

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

2380

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

2381

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

2382

\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0 \]

2383

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

2384

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \]

2385

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

2386

\[ {}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0 \]

2387

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

2388

\[ {}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0 \]

2389

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

2390

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

2391

\[ {}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

2392

\[ {}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0 \]

2393

\[ {}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \]

2394

\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }-5 x y^{\prime }+2 y = 0 \]

2395

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

2396

\[ {}\left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y = 0 \]

2397

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

2398

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

2399

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

2400

\[ {}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (1+x \right ) y = 0 \]