6.81 Problems 8001 to 8100

Table 6.161: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

8001

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

8002

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

8003

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

8004

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

8005

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

8006

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

8007

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

8008

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

8009

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

8010

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

8011

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

8012

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]

8013

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

8014

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

8015

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

8016

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

8017

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

8018

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

8019

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8 \]

8020

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

8021

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \]

8022

\[ {} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \]

8023

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

8024

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

8025

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

8026

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

8027

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

8028

\[ {} y^{\prime \prime }+5 y = \cos \left (x \sqrt {5}\right ) \]

8029

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

8030

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

8031

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

8032

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

8033

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

8034

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

8035

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

8036

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

8037

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

8038

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

8039

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

8040

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

8041

\[ {} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 6 x \]

8042

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

8043

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

8044

\[ {} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8 \]

8045

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

8046

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

8047

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

8048

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

8049

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

8050

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

8051

\[ {} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

8052

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

8053

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

8054

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

8055

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

8056

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

8057

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

8058

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

8059

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

8060

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

8061

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

8062

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

8063

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

8064

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

8065

\[ {} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

8066

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

8067

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

8068

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

8069

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

8070

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

8071

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

8072

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

8073

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

8074

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

8075

\[ {} [x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = {\mathrm e}^{t}+2, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1] \]

8076

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

8077

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

8078

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

8079

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

8080

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

8081

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

8082

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

8083

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

8084

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

8085

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

8086

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

8087

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

8088

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

8089

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

8090

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

8091

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

8092

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

8093

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

8094

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

8095

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

8096

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

8097

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

8098

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

8099

\[ {} z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0 \]

8100

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