3.9.26 Problems 2501 to 2600

Table 3.557: First order ode linear in derivative

#

ODE

Mathematica

Maple

5238

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

5239

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

5240

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

5241

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

5242

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

5243

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

5244

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

5245

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

5246

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

5247

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

5248

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

5249

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

5250

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

5251

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

5252

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

5253

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

5254

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

5255

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

5256

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

5257

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

5258

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

5259

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

5260

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

5261

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

5262

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

5263

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

5264

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

5265

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

5266

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

5267

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

5268

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

5269

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

5270

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

5271

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

5272

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

5273

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

5274

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

5275

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

5276

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

5277

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

5278

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

5279

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

5280

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

5281

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

5282

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

5283

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

5284

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

5285

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

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

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

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

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