3.1.31 Problems 3001 to 3100

Table 3.61: First order ode

#

ODE

Mathematica

Maple

5286

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

5287

\[ {}y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime } = 0 \]

5288

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

5289

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

5290

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

5291

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

5292

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

5293

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

5294

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

5295

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

5296

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

5297

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

5298

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

5299

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

5300

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

5301

\[ {}i^{\prime }-6 i = 10 \sin \left (2 t \right ) \]

5302

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

5303

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

5304

\[ {}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \]

5305

\[ {}x y^{\prime }+y-x^{3} y^{6} = 0 \]

5306

\[ {}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0 \]

5307

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

5308

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

5309

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

5310

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

5311

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

5312

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

5313

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

5314

\[ {}2 x y^{5}-y+2 x y^{\prime } = 0 \]

5315

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

5316

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

5317

\[ {}L i^{\prime }+R i = E \sin \left (2 t \right ) \]

5318

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

5319

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

5320

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

5321

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

5322

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

5323

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

5324

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

5325

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

5326

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

5327

\[ {}8 y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]

5328

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

5329

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

5330

\[ {}16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

5331

\[ {}x {y^{\prime }}^{5}-{y^{\prime }}^{4} y+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0 \]

5332

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

5333

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

5334

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

5335

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

5336

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

5337

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

5338

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

5339

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

5340

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

5341

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

5342

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

5343

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

5344

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

5345

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

5346

\[ {}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]

5347

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

5451

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

5499

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

5679

\[ {}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5} \]

5680

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

5691

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

5714

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

5715

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

5716

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

5717

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

5718

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

5719

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

5720

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

5721

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

5722

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

5723

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

5724

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

5725

\[ {}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1 \]

5726

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

5727

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

5728

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

5729

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

5730

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

5731

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

5732

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

5733

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

5734

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

5735

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

5736

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

5737

\[ {}z^{\prime } = 10^{x +z} \]

5738

\[ {}x^{\prime }+t = 1 \]

5739

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

5740

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

5741

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

5742

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

5743

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

5744

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

5745

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

5746

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