6.24 Problems 2301 to 2400

Table 6.47: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

2301

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

2302

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

2303

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

2304

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

2305

\[ {} \frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1} \]

2306

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

2307

\[ {} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]

2308

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

2309

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

2310

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

2311

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

2312

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

2313

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

2314

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

2315

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

2316

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

2317

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

2318

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

2319

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

2320

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

2321

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

2322

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

2323

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

2324

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

2325

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

2326

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

2327

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

2328

\[ {} y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]

2329

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

2330

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

2331

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

2332

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

2333

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

2334

\[ {} {\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \]

2335

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

2336

\[ {} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

2337

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

2338

\[ {} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \]

2339

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

2340

\[ {} \sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0 \]

2341

\[ {} \frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \]

2342

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

2343

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

2344

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

2345

\[ {} 2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0 \]

2346

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

2347

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

2348

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

2349

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

2350

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

2351

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

2352

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

2353

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

2354

\[ {} y^{\prime } = y^{3}+{\mathrm e}^{-5 t} \]

2355

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

2356

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

2357

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

2358

\[ {} y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \]

2359

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

2360

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

2361

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

2362

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

2363

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

2364

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

2365

\[ {} 6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

2366

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

2367

\[ {} 3 y^{\prime \prime }+6 y^{\prime }+3 y = 0 \]

2368

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

2369

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

2370

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

2371

\[ {} y^{\prime \prime }-6 y^{\prime }+y = 0 \]

2372

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

2373

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

2374

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

2375

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

2376

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

2377

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

2378

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

2379

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

2380

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

2381

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

2382

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

2383

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

2384

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

2385

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

2386

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

2387

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

2388

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

2389

\[ {} 9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

2390

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

2391

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

2392

\[ {} 9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

2393

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

2394

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

2395

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

2396

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

2397

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

2398

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

2399

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

2400

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