6.84 Problems 8301 to 8400

Table 6.167: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

8301

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

8302

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

8303

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

8304

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8305

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8306

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8307

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8308

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

8309

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

8310

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

8311

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

8312

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

8313

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

8314

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

8315

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

8316

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

8317

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

8318

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

8319

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

8320

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

8321

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

8322

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

8323

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

8324

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

8325

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

8326

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

8327

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

8328

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

8329

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

8330

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

8331

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

8332

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

8333

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

8334

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

8335

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

8336

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

8337

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

8338

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

8339

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

8340

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

8341

\[ {} y^{\prime } = 10+3 y-y^{2} \]

8342

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

8343

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

8344

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

8345

\[ {} y^{\prime } = \left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \]

8346

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

8347

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

8348

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

8349

\[ {} y^{\prime } = \sin \left (5 x \right ) \]

8350

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

8351

\[ {} 1+{\mathrm e}^{3 x} y^{\prime } = 0 \]

8352

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

8353

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

8354

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

8355

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

8356

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

8357

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

8358

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

8359

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

8360

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

8361

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

8362

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

8363

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

8364

\[ {} q^{\prime } = k \left (q-70\right ) \]

8365

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

8366

\[ {} n^{\prime }+n = n t \,{\mathrm e}^{t +2} \]

8367

\[ {} y^{\prime } = \frac {x y+3 x -y-3}{x y-2 x +4 y-8} \]

8368

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

8369

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

8370

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

8371

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

8372

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

8373

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

8374

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

8375

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

8376

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

8377

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

8378

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

8379

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

8380

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

8381

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

8382

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

8383

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

8384

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

8385

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

8386

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

8387

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

8388

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

8389

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

8390

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

8391

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

8392

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

8393

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

8394

\[ {} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime } = 0 \]

8395

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

8396

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

8397

\[ {} y^{\prime } = \left (y-1\right )^{2}+\frac {1}{100} \]

8398

\[ {} y^{\prime } = \left (y-1\right )^{2}-\frac {1}{100} \]

8399

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

8400

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