2.74 Problems 7301 to 7400

Table 2.147: Main lookup table

#

ODE

Mathematica result

Maple result

7301

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

7302

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

7303

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

7304

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

7305

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

7306

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

7307

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

7308

\[ {}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2} \]

7309

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

7310

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

7311

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

7312

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

7313

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

7314

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

7315

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

7316

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

7317

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

7318

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

7319

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

7320

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

7321

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

7322

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

7323

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

7324

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

7325

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

7326

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

7327

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

7328

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

7329

\[ {}c y^{\prime } = a \]

7330

\[ {}c y^{\prime } = a x \]

7331

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

7332

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

7333

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

7334

\[ {}c y^{\prime } = b y \]

7335

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

7336

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r} \]

7337

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r x} \]

7338

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}} \]

7339

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

7340

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

7341

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

7342

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

7343

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

7344

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

7345

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

7346

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

7347

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

7348

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

7349

\[ {}{\mathrm e} y^{\prime } = 0 \]

7350

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

7351

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

7352

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

7353

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

7354

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

7355

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

7356

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

7357

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

7358

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

7359

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

7360

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

7361

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

7362

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

7363

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

7364

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

7365

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

7366

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

7367

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

7368

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

7369

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

7370

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

7371

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

7372

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

7373

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

7374

\[ {}{y^{\prime }}^{4} = \frac {1}{x y^{3}} \]

7375

\[ {}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}} \]

7376

\[ {}y^{\prime } = \sqrt {1+6 x +y} \]

7377

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

7378

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

7379

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

7380

\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{\frac {7}{2}} \]

7381

\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]

7382

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

7383

\[ {}y^{\prime } = 10+{\mathrm e}^{x +y} \]

7384

\[ {}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2} \]

7385

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

7386

\[ {}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \]

7387

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

7388

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

7389

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

7390

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

7391

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

7392

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

7393

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

7394

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

7395

\[ {}a {y^{\prime \prime }}^{n} = 0 \]

7396

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

7397

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

7398

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

7399

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

7400

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