4.1.31 Problems 3001 to 3100

Table 4.61: First order ode

#

ODE

Mathematica

Maple

Sympy

6019

\[ {} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0 \]

6020

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

6021

\[ {} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

6022

\[ {} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

6023

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

6024

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

6025

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

6027

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

6028

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

6029

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

6031

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

6032

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

6033

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

6034

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

6035

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

6036

\[ {} y^{\prime }+b^{2} y^{2} = a^{2} \]

6037

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

6038

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

6039

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

6075

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

6092

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

6093

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

6094

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

6095

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

6096

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

6097

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

6098

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

6099

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

6100

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

6101

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

6102

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

6103

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

6104

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

6105

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

6106

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

6107

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

6108

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

6109

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

6110

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

6111

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

6112

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

6113

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

6114

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

6115

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

6116

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

6117

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

6118

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

6119

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

6120

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

6121

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

6122

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

6123

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

6124

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

6125

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

6126

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

6127

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

6128

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

6129

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

6130

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

6131

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

6132

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

6133

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

6134

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

6208

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

6209

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

6212

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

6214

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

6216

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

6217

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

6218

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

6224

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

6225

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

6226

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

6228

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

6230

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

6232

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

6233

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

6237

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

6239

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

6241

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

6256

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

6257

\[ {} y^{\prime } = 4 y^{2}-3 y+1 \]

6258

\[ {} s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

6259

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

6260

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

6261

\[ {} s^{2}+s^{\prime } = \frac {s+1}{s t} \]

6262

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

6263

\[ {} x^{\prime } = 3 x t^{2} \]

6264

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

6265

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

6266

\[ {} x v^{\prime } = \frac {1-4 v^{2}}{3 v} \]

6267

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

6268

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

6269

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

6270

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

6271

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

6272

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

6273

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

6274

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

6275

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