4.1.82 Problems 8101 to 8200

Table 4.163: First order ode

#

ODE

Mathematica

Maple

Sympy

18786

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

18787

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

18968

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

18969

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

18970

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

18971

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

18972

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

18973

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

18974

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

18975

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

18976

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

18977

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

18978

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

18979

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

18980

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

18981

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

18982

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

18983

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

18984

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

18985

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

18986

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

18987

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

18988

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

18989

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

18990

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

18991

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

18992

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

18993

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

18994

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

18995

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

18996

\[ {} \left (2 x +3 y-5\right ) y^{\prime }+2 x +3 y-1 = 0 \]

18997

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

18998

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

18999

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

19000

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

19001

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

19002

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

19003

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

19004

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

19005

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

19006

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

19007

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

19008

\[ {} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

19009

\[ {} \left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

19010

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

19011

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

19012

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

19013

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

19014

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

19015

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

19016

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

19017

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

19018

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

19019

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

19020

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

19021

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

19022

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

19023

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

19024

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

19025

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

19026

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

19027

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

19028

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

19029

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

19030

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

19031

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

19032

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

19033

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

19034

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

19035

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

19036

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

19037

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

19038

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

19039

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

19040

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

19041

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

19042

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

19043

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

19044

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

19045

\[ {} \left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0 \]

19046

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

19047

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

19048

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

19049

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

19050

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

19051

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

19052

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

19053

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

19054

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

19055

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

19056

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

19057

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

19058

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

19059

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

19060

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

19061

\[ {} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \]

19062

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

19063

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

19064

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

19065

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