6.194 Problems 19301 to 19400

Table 6.387: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19301

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

19302

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

19303

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} \]

19304

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

19305

\[ {} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = {\mathrm e}^{x} \left (1+x \right ) \]

19306

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

19307

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

19308

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

19309

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

19310

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

19311

\[ {} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \]

19312

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

19313

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \]

19314

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

19315

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

19316

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

19317

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

19318

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

19319

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

19320

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

19321

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

19322

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

19323

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

19324

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

19325

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

19326

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

19327

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

19328

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

19329

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

19330

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

19331

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

19332

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

19333

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

19334

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

19335

\[ {} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = 7 \,{\mathrm e}^{t}-27, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = -3 \,{\mathrm e}^{t}+12] \]

19336

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

19337

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

19338

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

19339

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

19340

\[ {} [t x^{\prime }\left (t \right )+6 x \left (t \right )-y \left (t \right )-3 z \left (t \right ) = 0, t y^{\prime }\left (t \right )+23 x \left (t \right )-6 y \left (t \right )-9 z \left (t \right ) = 0, t z^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )-2 z \left (t \right ) = 0] \]

19341

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

19342

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

19343

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

19344

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

19345

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

19346

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

19347

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

19348

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

19349

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

19350

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

19351

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

19352

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

19353

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

19354

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

19355

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

19356

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

19357

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

19358

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

19359

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

19360

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

19361

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

19362

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

19363

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

19364

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

19365

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

19366

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

19367

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

19368

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

19369

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

19370

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

19371

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

19372

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

19373

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

19374

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

19375

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

19376

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

19377

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

19378

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

19379

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

19380

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

19381

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

19382

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

19383

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

19384

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

19385

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

19386

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

19387

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

19388

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

19389

\[ {} v^{\prime } = g -\frac {k v^{2}}{m} \]

19390

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

19391

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

19392

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

19393

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

19394

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

19395

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

19396

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

19397

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

19398

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

19399

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

19400

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