4.9.67 Problems 6601 to 6700

Table 4.971: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

18080

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

18081

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

18082

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

18083

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

18084

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

18085

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

18086

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

18087

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

18088

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

18089

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

18090

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

18091

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

18092

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

18093

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

18094

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

18095

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

18096

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

18097

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

18098

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

18099

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

18100

\[ {} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]

18101

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

18102

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

18103

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

18135

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

18136

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

18137

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

18138

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

18143

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

18154

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

18155

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

18156

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

18157

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

18158

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

18159

\[ {} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \]

18160

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

18161

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

18162

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

18163

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

18164

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

18165

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

18166

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

18167

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

18168

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

18169

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

18170

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

18171

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

18172

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

18173

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

18174

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

18175

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

18176

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

18177

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

18178

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

18179

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

18180

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

18181

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

18182

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

18183

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

18184

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

18185

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

18186

\[ {} y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \]

18187

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

18188

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

18189

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

18190

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

18570

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

18571

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

18572

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

18573

\[ {} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

18574

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

18587

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

18588

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

18589

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

18590

\[ {} y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]

18591

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

18592

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

18593

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

18594

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

18595

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

18596

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

18597

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

18598

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

18599

\[ {} y^{\prime } = \left (1-12 x \right ) y^{2} \]

18600

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

18601

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

18602

\[ {} r^{\prime } = \frac {r^{2}}{\theta } \]

18603

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

18604

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

18605

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

18606

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

18607

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

18608

\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]

18609

\[ {} y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \]

18610

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

18611

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

18612

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

18613

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

18614

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

18615

\[ {} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \]