4.9.85 Problems 8401 to 8500

Table 4.1007: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

24024

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

24025

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

24026

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

24027

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

24028

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

24029

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

24030

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

24031

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

24032

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

24033

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

24034

\[ {} y^{5} y^{\prime }+5 y^{6} = 1 \]

24035

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

24057

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

24058

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

24060

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

24061

\[ {} y^{\prime } = \frac {1}{x^{5}+x y} \]

24062

\[ {} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime } = 0 \]

24063

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

24064

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

24065

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

24066

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

24069

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

24071

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

24072

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

24073

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

24074

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

24075

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

24076

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

24077

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

24079

\[ {} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime } = 0 \]

24081

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

24084

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

24085

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

24086

\[ {} y^{\prime }-5 y = 3 x^{3}+4 x \]

24087

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

24088

\[ {} y^{\prime }-x y = -x^{5}+4 x^{3} \]

24173

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

24236

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

24237

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

24238

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

24239

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

24240

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

24241

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

24242

\[ {} v^{\prime } = -\frac {v}{p} \]

24243

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

24244

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

24245

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

24246

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

24247

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

24248

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

24249

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

24250

\[ {} \theta ^{\prime } = z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \]

24251

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

24252

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

24253

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

24254

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

24255

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

24256

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

24257

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

24258

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

24259

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

24260

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

24261

\[ {} r^{\prime } = -2 r t \]

24262

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

24263

\[ {} \left (2 a^{2}-r^{2}\right ) r^{\prime } = r^{3} \sin \left (\theta \right ) \]

24264

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

24265

\[ {} v v^{\prime } = g \]

24266

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

24267

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

24268

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

24269

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

24270

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

24271

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

24272

\[ {} 5 v-u +\left (3 v-7 u \right ) v^{\prime } = 0 \]

24273

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

24274

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

24275

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

24276

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

24277

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

24278

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

24279

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

24280

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

24281

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

24282

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

24283

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

24284

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

24285

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

24286

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

24287

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

24288

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

24289

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

24290

\[ {} y^{2}+7 x y+16 x^{2}+x^{2} y^{\prime } = 0 \]

24291

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

24292

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

24293

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

24294

\[ {} y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime } = 0 \]

24295

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

24296

\[ {} 16 x +15 y+\left (3 x +y\right ) y^{\prime } = 0 \]

24297

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

24298

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