4.9.69 Problems 6801 to 6900

Table 4.975: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

18716

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

18717

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

18718

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

18719

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

18720

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

18721

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

18722

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

18723

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

18724

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

18725

\[ {} 3 t y^{\prime }+9 y = 2 t y^{{5}/{3}} \]

18726

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

18727

\[ {} y^{\prime } = r y-k^{2} y^{2} \]

18728

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

18729

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

18730

\[ {} \left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

18731

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

18732

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

18733

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

18734

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

18735

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

18736

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

18737

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

18738

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

18739

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

18740

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

18741

\[ {} 4 y y^{\prime } x = 8 x^{2}+5 y^{2} \]

18742

\[ {} y^{\prime }+y-y^{{1}/{4}} = 0 \]

18830

\[ {} x^{\prime } = \frac {x \sqrt {6 x-9}}{3} \]

19177

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

19178

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

19180

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

19181

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

19182

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

19183

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

19184

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

19185

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

19186

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

19187

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

19188

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

19189

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

19190

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

19191

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

19192

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

19193

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

19194

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

19195

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

19196

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

19197

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

19198

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

19199

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

19200

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

19201

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

19202

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

19203

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

19204

\[ {} y^{\prime } = y^{2}+\frac {1}{x^{4}} \]

19205

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

19206

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

19207

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

19208

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

19209

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

19210

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

19211

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

19212

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

19213

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

19214

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

19215

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

19216

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

19217

\[ {} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

19218

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

19219

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

19220

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

19221

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

19241

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

19242

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

19243

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

19244

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

19245

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

19246

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

19247

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

19342

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

19343

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

19344

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

19345

\[ {} y^{\prime } = k y \]

19348

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

19349

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

19350

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

19351

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

19353

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

19354

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

19355

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

19356

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

19357

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

19358

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

19359

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

19360

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

19361

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

19362

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

19363

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

19364

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

19365

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