4.9.16 Problems 1501 to 1600

Table 4.869: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

4307

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

4308

\[ {} y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )} \]

4309

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

4310

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

4311

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

4312

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

4313

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

4314

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

4315

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

4316

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

4317

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

4318

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

4319

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

4320

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

4321

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

4322

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

4323

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

4324

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

4325

\[ {} y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \]

4326

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

4327

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

4328

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

4329

\[ {} 3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \]

4330

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

4331

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

4332

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

4333

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

4334

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

4335

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

4336

\[ {} 4 x y+3 y^{2}-x +x \left (2 y+x \right ) y^{\prime } = 0 \]

4337

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

4338

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

4339

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

4340

\[ {} 3 y^{2}+3 x^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0 \]

4341

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

4342

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

4343

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

4344

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

4345

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

4346

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

4347

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

4348

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

4349

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

4350

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

4351

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

4352

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

4353

\[ {} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0 \]

4354

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

4355

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

4356

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

4357

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

4358

\[ {} 2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0 \]

4359

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

4360

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

4361

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

4362

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

4363

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

4364

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

4365

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

4366

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

4367

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

4368

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

4369

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

4370

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

4371

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

4372

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

4373

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

4374

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

4375

\[ {} 3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \]

4376

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

4377

\[ {} y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \]

4378

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

4379

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

4380

\[ {} 2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0 \]

4381

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

4382

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

4396

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

4398

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

4399

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

4400

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

4401

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

4403

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

4404

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

4405

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

4406

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

4408

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

4409

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

4410

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

4411

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

4412

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

4415

\[ {} y+3 x^{4} y^{2}+\left (x +2 x^{2} y^{3}\right ) y^{\prime } = 0 \]

4416

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

4417

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

4418

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

4419

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

4420

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

4421

\[ {} 2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7 = 0 \]

4422

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

4423

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

4424

\[ {} y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime } = 0 \]