6.201 Problems 20001 to 20100

Table 6.401: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

20001

\[ {} [y^{\prime }\left (x \right )+z^{\prime }\left (x \right )+6 y \left (x \right ) = 0, z^{\prime }\left (x \right )+5 y \left (x \right )+z \left (x \right ) = 0] \]

20002

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

20003

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

20004

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

20005

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

20006

\[ {} [z^{\prime }\left (x \right )+7 y \left (x \right )-9 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )-y \left (x \right )-3 z \left (x \right ) = {\mathrm e}^{2 x}] \]

20007

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

20008

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

20009

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

20010

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

20011

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

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

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

20068

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

20069

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

20070

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

20071

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

20072

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

20073

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

20074

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

20075

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

20076

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

20077

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

20078

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

20079

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

20080

\[ {} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

20081

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

20082

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

20083

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

20084

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

20085

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

20086

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

20087

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

20088

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

20089

\[ {} {y^{\prime }}^{3} = a \,x^{4} \]

20090

\[ {} 4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0 \]

20091

\[ {} {y^{\prime }}^{2}-7 y^{\prime }+12 = 0 \]

20092

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

20093

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

20094

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

20095

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

20096

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

20097

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

20098

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

20099

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

20100

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