6.74 Problems 7301 to 7400

Table 6.147: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7301

\[ {} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

7302

\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

7303

\[ {} y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

7304

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

7305

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

7306

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

7307

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

7308

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

7309

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \]

7310

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

7311

\[ {} y^{\prime \prime }+y = 8 x \sin \left (x \right ) \]

7312

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

7313

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{x}+6 x -5 \]

7314

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

7315

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

7316

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

7317

\[ {} y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

7318

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

7319

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

7320

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

7321

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

7322

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

7323

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

7324

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

7325

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

7326

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

7327

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

7328

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

7329

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

7330

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

7331

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

7332

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

7333

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

7334

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right ) \]

7335

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

7336

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

7337

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

7338

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

7339

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

7340

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

7341

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

7342

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

7343

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

7344

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

7345

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

7346

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

7347

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

7348

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

7349

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

7350

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

7351

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

7352

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

7353

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

7354

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

7355

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 26 \,{\mathrm e}^{3 x} \]

7356

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

7357

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

7358

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x} \]

7359

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

7360

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

7361

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

7362

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]

7363

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

7364

\[ {} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

7365

\[ {} \sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2} \]

7366

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

7367

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

7368

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

7369

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

7370

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

7371

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

7372

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

7373

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

7374

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

7375

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

7376

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

7377

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

7378

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

7379

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

7380

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

7381

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

7382

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

7383

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

7384

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

7385

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

7386

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

7387

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

7388

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

7389

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

7390

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

7391

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

7392

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

7393

\[ {} s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

7394

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

7395

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

7396

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

7397

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

7398

\[ {} x^{\prime } = 3 x t^{2} \]

7399

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

7400

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