3.9.53 Problems 5201 to 5300

Table 3.611: First order ode linear in derivative

#

ODE

Mathematica

Maple

13303

\[ {}y^{\prime }+4 y = 8 \]

13304

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

13305

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

13306

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

13307

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

13308

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

13309

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

13310

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

13311

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

13312

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

13313

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

13314

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

13315

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

13316

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

13317

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

13318

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

13319

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

13320

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

13321

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

13322

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

13323

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

13324

\[ {}y^{\prime } = 200 y-2 y^{2} \]

13325

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

13326

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

13327

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

13328

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

13329

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

13330

\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]

13331

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

13332

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

13333

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

13334

\[ {}y^{\prime } = {\mathrm e}^{-y}+1 \]

13335

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

13336

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

13337

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

13338

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

13339

\[ {}y^{\prime } = 200 y-2 y^{2} \]

13340

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

13341

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

13342

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

13343

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

13344

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

13345

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

13346

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

13347

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

13348

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

13349

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

13350

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

13351

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

13352

\[ {}y^{\prime } = 4 y+8 \]

13353

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

13354

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

13355

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

13356

\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \]

13357

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

13358

\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \]

13359

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

13360

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

13361

\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \]

13362

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

13363

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

13364

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

13365

\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \]

13366

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

13367

\[ {}y^{\prime }-3 y = 6 \]

13368

\[ {}y^{\prime }-3 y = 6 \]

13369

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

13370

\[ {}x y^{\prime }+3 y = 20 x^{2} \]

13371

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

13372

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

13373

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

13374

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

13375

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

13376

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

13377

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

13378

\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \]

13379

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

13380

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

13381

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

13382

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

13383

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

13384

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

13385

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

13386

\[ {}y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{\frac {2}{3}} \]

13387

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

13388

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

13389

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

13390

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

13391

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

13392

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

13393

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

13394

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

13395

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

13396

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

13397

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

13398

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

13399

\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

13400

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

13401

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

13402

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