6.221 Problems 22001 to 22100

Table 6.441: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

22001

\[ {} y^{\prime \prime }-y^{\prime } = 6 x^{5} {\mathrm e}^{x} \]

22002

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

22003

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

22004

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = x^{3}+{\mathrm e}^{x} \]

22005

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

22006

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

22007

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

22008

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

22009

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

22010

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

22011

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

22012

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

22013

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

22014

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

22015

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

22016

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

22017

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

22018

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

22019

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

22020

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

22021

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

22022

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

22023

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

22024

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

22025

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

22026

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

22027

\[ {} y^{\prime \prime }-4 y = 0 \]

22028

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

22029

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

22030

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

22031

\[ {} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right ) \]

22032

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

22033

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime } = 0 \]

22034

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

22035

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

22036

\[ {} y^{\prime \prime }+4 y = t \sin \left (t \right ) \]

22037

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

22038

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

22039

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0 \]

22040

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

22041

\[ {} [x^{\prime \prime }\left (t \right ) = 1, x^{\prime }\left (t \right )+x \left (t \right )+y^{\prime \prime }\left (t \right )-9 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 0, 5 x \left (t \right )+z^{\prime \prime }\left (t \right )-4 z \left (t \right ) = 2] \]

22042

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

22043

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

22044

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

22045

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

22046

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

22047

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

22048

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

22049

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

22050

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

22051

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

22052

\[ {} x y^{\prime \prime }+y^{\prime } = 16 x^{3} \]

22053

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

22054

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

22055

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

22056

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

22057

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

22058

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

22059

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

22060

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

22061

\[ {} y^{\prime \prime }+4 y = 2 t -8 \]

22062

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

22063

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

22064

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = 6 \]

22065

\[ {} y^{\prime \prime \prime }-5 x y^{\prime } = {\mathrm e}^{x}+1 \]

22066

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

22067

\[ {} s^{2} t^{\prime \prime }+s t t^{\prime } = s \]

22068

\[ {} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5} = p \]

22069

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

22070

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

22071

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

22072

\[ {} t^{2} s^{\prime \prime }-t s^{\prime } = 1-\sin \left (t \right ) \]

22073

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

22074

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

22075

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

22076

\[ {} b^{\left (7\right )} = 3 p \]

22077

\[ {} {b^{\prime }}^{7} = 3 p \]

22078

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

22079

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

22080

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

22081

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

22082

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

22083

\[ {} 4 y+y^{\prime \prime } = 0 \]

22084

\[ {} 4 y+y^{\prime \prime } = 0 \]

22085

\[ {} 4 y+y^{\prime \prime } = 0 \]

22086

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

22087

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

22088

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

22089

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

22090

\[ {} y^{\prime } = 5 \]

22091

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

22092

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

22093

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

22094

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

22095

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

22096

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

22097

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

22098

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

22099

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

22100

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