6.204 Problems 20301 to 20400

Table 6.407: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

20301

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

20302

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

20303

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

20304

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

20305

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

20306

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0 \]

20307

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

20308

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

20309

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

20310

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

20311

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

20312

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

20313

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

20314

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

20315

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

20316

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

20317

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

20318

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

20319

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

20320

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

20321

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

20322

\[ {} [x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0] \]

20323

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

20324

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}] \]

20325

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

20326

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

20327

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3] \]

20328

\[ {} [x^{\prime }\left (t \right )+4 x \left (t \right )+3 y \left (t \right ) = t, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = {\mathrm e}^{t}] \]

20329

\[ {} [x^{\prime }\left (t \right ) = n y \left (t \right )-m z \left (t \right ), y^{\prime }\left (t \right ) = L z \left (t \right )-m x \left (t \right ), z^{\prime }\left (t \right ) = m x \left (t \right )-L y \left (t \right )] \]

20330

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

20331

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

20332

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

20333

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

20334

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

20335

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

20336

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

20337

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

20338

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

20339

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

20340

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

20341

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

20342

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

20343

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

20344

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

20345

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

20346

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

20347

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

20348

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

20349

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

20350

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

20351

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

20352

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

20353

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

20354

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

20355

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

20356

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

20357

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

20358

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

20359

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

20360

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

20361

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

20362

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

20363

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

20364

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

20365

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

20366

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

20367

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

20368

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

20369

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

20370

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

20371

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

20372

\[ {} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

20373

\[ {} \left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

20374

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

20375

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

20376

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

20377

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

20378

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

20379

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

20380

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

20381

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

20382

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

20383

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

20384

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

20385

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

20386

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

20387

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

20388

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

20389

\[ {} y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}} \]

20390

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

20391

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

20392

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

20393

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

20394

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

20395

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

20396

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

20397

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

20398

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

20399

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

20400

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