2.114 Problems 11301 to 11400

Table 2.227: Main lookup table

#

ODE

Mathematica result

Maple result

11301

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

11302

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

11303

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

11304

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

11305

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

11306

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

11307

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

11308

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

11309

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

11310

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \]

11311

\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \]

11312

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

11313

\[ {}\left (-3+x \right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

11314

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

11315

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

11316

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

11317

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

11318

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

11319

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

11320

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

11321

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

11322

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

11323

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

11324

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

11325

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

11326

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

11327

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

11328

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

11329

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

11330

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

11331

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

11332

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

11333

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

11334

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

11335

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

11336

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

11337

\[ {}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0 \]

11338

\[ {}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \]

11339

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

11340

\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

11341

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

11342

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

11343

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

11344

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

11345

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

11346

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

11347

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

11348

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

11349

\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \]

11350

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

11351

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

11352

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

11353

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

11354

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

11355

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

11356

\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \]

11357

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

11358

\[ {}[3 x^{\prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{t}, 4 x \left (t \right )-3 y^{\prime }\left (t \right )+3 y \left (t \right ) = 3 t] \]

11359

\[ {}x^{\prime } = \frac {2 x}{t} \]

11360

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

11361

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

11362

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

11363

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

11364

\[ {}x^{\prime }+2 x = t^{2}+4 t +7 \]

11365

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

11366

\[ {}t^{2} x^{\prime \prime }-6 x = 0 \]

11367

\[ {}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \]

11368

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

11369

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

11370

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

11371

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

11372

\[ {}x^{\prime \prime } = -3 \sqrt {t} \]

11373

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

11374

\[ {}x^{\prime } = \frac {1}{t \ln \left (t \right )} \]

11375

\[ {}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

11376

\[ {}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

11377

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

11378

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

11379

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

11380

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

11381

\[ {}u^{\prime } = \frac {1}{5-2 u} \]

11382

\[ {}x^{\prime } = a x+b \]

11383

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

11384

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

11385

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

11386

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

11387

\[ {}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

11388

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

11389

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

11390

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

11391

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

11392

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

11393

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

11394

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

11395

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

11396

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

11397

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

11398

\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]

11399

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

11400

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