6.211 Problems 21001 to 21100

Table 6.421: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

21001

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

21002

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

21003

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

21004

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

21005

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

21006

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

21007

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

21008

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

21009

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

21010

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

21011

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

21012

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

21013

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

21014

\[ {} \frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{x +6}+\frac {x^{2} \left (x -2\right ) y}{x -1} = 0 \]

21015

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

21016

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

21017

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

21018

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

21019

\[ {} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0 \]

21020

\[ {} y^{\prime \prime }+\frac {y}{4 x^{2}} = 0 \]

21021

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

21022

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

21023

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

21024

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

21025

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

21026

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

21027

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

21028

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

21029

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

21030

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

21031

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

21032

\[ {} y^{\prime \prime }-3 y^{\prime }-4 y = t^{2} \]

21033

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

21034

\[ {} y^{\prime \prime }+4 y = \delta \left (t -1\right ) \]

21035

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right ) \]

21036

\[ {} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right ) \]

21037

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

21038

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

21039

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

21040

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

21041

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

21042

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )] \]

21043

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

21044

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

21045

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

21046

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

21047

\[ {} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )] \]

21048

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

21049

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

21050

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

21051

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

21052

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

21053

\[ {} [x^{\prime }\left (t \right ) = 12 x \left (t \right )-15 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )] \]

21054

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

21055

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right )] \]

21056

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

21057

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

21058

\[ {} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 16 x \left (t \right )+8 y \left (t \right )] \]

21059

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

21060

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

21061

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

21062

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right )+1, y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t}] \]

21063

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

21064

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

21065

\[ {} y^{\prime } = y^{2}-6 y-16 \]

21066

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

21067

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

21068

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

21069

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

21070

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

21071

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

21072

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

21073

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

21074

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

21075

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

21076

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

21077

\[ {} x^{\prime } = x^{3}+a x^{2}-b x \]

21078

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

21079

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

21080

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

21081

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

21082

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

21083

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

21084

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

21085

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

21086

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

21087

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

21088

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

21089

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

21090

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

21091

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

21092

\[ {} y^{\prime }-y+y^{2} {\mathrm e}^{x}+5 \,{\mathrm e}^{-x} = 0 \]

21093

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

21094

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

21095

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

21096

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

21097

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

21098

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

21099

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

21100

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