6.71 Problems 7001 to 7100

Table 6.141: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7001

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

7002

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

7003

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

7004

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

7005

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

7006

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

7007

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

7008

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

7009

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

7010

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

7011

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

7012

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

7013

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

7014

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

7015

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

7016

\[ {} y^{\prime }+a y = k \,{\mathrm e}^{b x} \]

7017

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

7018

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

7019

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

7020

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

7021

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

7022

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

7023

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

7024

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

7025

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

7026

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

7027

\[ {} x y^{\prime }+a y+b \,x^{n} = 0 \]

7028

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

7029

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

7030

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

7031

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

7032

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

7033

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

7034

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

7035

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

7036

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

7037

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

7038

\[ {} y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

7039

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

7040

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

7041

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

7042

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

7043

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

7044

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

7045

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

7046

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

7047

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

7048

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

7049

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

7050

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

7051

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

7052

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

7053

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

7054

\[ {} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

7055

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

7056

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

7057

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

7058

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

7059

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

7060

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

7061

\[ {} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

7062

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

7063

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

7064

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

7065

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

7066

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

7067

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

7068

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

7069

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

7070

\[ {} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

7071

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

7072

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

7073

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

7074

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

7075

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

7076

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

7077

\[ {} y^{\prime \prime \prime }+8 y = 0 \]

7078

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

7079

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

7080

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

7081

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

7082

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

7083

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

7084

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

7085

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

7086

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

7087

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

7088

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

7089

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

7090

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

7091

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

7092

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

7093

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

7094

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

7095

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

7096

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

7097

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

7098

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

7099

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

7100

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