4.9.72 Problems 7101 to 7200

Table 4.981: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

19857

\[ {} v^{\prime }+\frac {2 v}{u} = 3 v \]

19858

\[ {} \sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}} \]

19860

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

19861

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

19862

\[ {} v^{\prime }+2 u v = 2 u \]

19863

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

19864

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

19874

\[ {} 5 x^{\prime }+x = \sin \left (3 t \right ) \]

19890

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

19905

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

19906

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

19907

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

19908

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

19909

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

19910

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

19911

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

19912

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

19913

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

19914

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

19915

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

19916

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

19917

\[ {} y^{\prime }-y \tan \left (x \right ) = y^{4} \sec \left (x \right ) \]

19918

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

19919

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

19920

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

19921

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

19922

\[ {} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0 \]

19923

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

19924

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

19925

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

19926

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

19927

\[ {} 5 y y^{\prime } x -x^{2}-y^{2} = 0 \]

19928

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

19929

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

19930

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

19931

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

19932

\[ {} \left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6 \]

19933

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

19934

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2 \]

19935

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

19936

\[ {} \left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7 \]

19937

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6 \]

19938

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

19939

\[ {} \left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1 \]

20012

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

20013

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

20014

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

20015

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

20016

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

20017

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

20018

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

20019

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

20020

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

20021

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

20022

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

20023

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

20024

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

20025

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

20026

\[ {} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0 \]

20027

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

20028

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

20029

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

20030

\[ {} x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0 \]

20031

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

20032

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

20033

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

20034

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

20035

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

20036

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

20037

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

20038

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

20039

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

20040

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

20041

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

20042

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

20043

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

20044

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

20045

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

20046

\[ {} y^{\prime }+\frac {y}{x} = y^{6} x^{2} \]

20047

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

20048

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

20049

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

20050

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

20051

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

20052

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

20053

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

20054

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

20055

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

20056

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

20057

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

20058

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

20059

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

20060

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

20061

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

20062

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

20063

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

20064

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

20065

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

20066

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

20067

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