4.1.75 Problems 7401 to 7500

Table 4.149: First order ode

#

ODE

Mathematica

Maple

Sympy

17970

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

17971

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

17972

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

17973

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

17974

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

17975

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

17976

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

17977

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

17978

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

17979

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

17980

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

17981

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

17982

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

17983

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

17984

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

17985

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

17986

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

17987

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

17988

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

17989

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

17990

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

17991

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

17992

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

17993

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

17994

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

17995

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

17996

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

17997

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

17998

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

17999

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

18000

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

18001

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

18002

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

18003

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

18004

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

18005

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

18006

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

18007

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

18008

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

18009

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

18010

\[ {} {\mathrm e}^{y^{\prime }} = 1 \]

18011

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

18012

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

18013

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

18014

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

18015

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

18016

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

18017

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

18018

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

18019

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

18020

\[ {} {\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \]

18021

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

18022

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

18023

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

18024

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

18025

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

18026

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

18027

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

18028

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

18029

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

18030

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

18031

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

18032

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

18033

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

18034

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

18035

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

18036

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

18037

\[ {} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

18038

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

18039

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

18040

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

18041

\[ {} 4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

18042

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

18043

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

18044

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

18045

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

18046

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

18047

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

18048

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

18049

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

18050

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

18051

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

18052

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

18053

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

18054

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

18055

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

18056

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

18057

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

18058

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

18059

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

18060

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

18061

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

18062

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

18063

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

18064

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

18065

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

18066

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

18067

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

18068

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

18069

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