6.81 Problems 8001 to 8100

Table 6.161: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

8001

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

8002

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

8003

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

8004

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

8005

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

8006

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

8007

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

8008

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

8009

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

8010

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

8011

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

8012

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

8013

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

8014

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

8015

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

8016

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

8017

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]

8018

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

8019

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

8020

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

8021

\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

8022

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

8023

\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \]

8024

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

8025

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

8026

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

8027

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]

8028

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

8029

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]

8030

\[ {} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0 \]

8031

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

8032

\[ {} y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

8033

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

8034

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

8035

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

8036

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

8037

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

8038

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

8039

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

8040

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

8041

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

8042

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

8043

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

8044

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

8045

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

8046

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

8047

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

8048

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

8049

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

8050

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

8051

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

8052

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

8053

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

8054

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

8055

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

8056

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

8057

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

8058

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

8059

\[ {} y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

8060

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

8061

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

8062

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

8063

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

8064

\[ {} y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \]

8065

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

8066

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

8067

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

8068

\[ {} y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \]

8069

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

8070

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

8071

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

8072

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

8073

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

8074

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

8075

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

8076

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

8077

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

8078

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

8079

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

8080

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

8081

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

8082

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

8083

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

8084

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

8085

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

8086

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

8087

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

8088

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

8089

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

8090

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

8091

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

8092

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

8093

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

8094

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

8095

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

8096

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

8097

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

8098

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

8099

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

8100

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