6.71 Problems 7001 to 7100

Table 6.141: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7001

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

7002

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

7003

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

7004

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

7005

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

7006

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

7007

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

7008

\[ {} y^{\prime \prime }+9 y = 5 \]

7009

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

7010

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]

7011

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]

7012

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]

7013

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]

7014

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

7015

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

7016

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

7017

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

7018

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7019

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7020

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7021

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7022

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

7023

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

7024

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

7025

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

7026

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

7027

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

7028

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

7029

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

7030

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

7031

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

7032

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

7033

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

7034

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

7035

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

7036

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

7037

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

7038

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

7039

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

7040

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

7041

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

7042

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

7043

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

7044

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

7045

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

7046

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

7047

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

7048

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

7049

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

7050

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

7051

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

7052

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

7053

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

7054

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

7055

\[ {} y^{\prime } = 10+3 y-y^{2} \]

7056

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

7057

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

7058

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

7059

\[ {} y^{\prime } = \left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \]

7060

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

7061

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

7062

\[ {} m v^{\prime } = m g -k v^{2} \]

7063

\[ {} y^{\prime } = \sin \left (5 x \right ) \]

7064

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

7065

\[ {} 1+{\mathrm e}^{3 x} y^{\prime } = 0 \]

7066

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

7067

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

7068

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

7069

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

7070

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

7071

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

7072

\[ {} y^{\prime } = \frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}} \]

7073

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

7074

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

7075

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

7076

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

7077

\[ {} s^{\prime } = k s \]

7078

\[ {} q^{\prime } = k \left (q-70\right ) \]

7079

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

7080

\[ {} n^{\prime }+n = n t \,{\mathrm e}^{t +2} \]

7081

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

7082

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

7083

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

7084

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

7085

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

7086

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

7087

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

7088

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

7089

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

7090

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

7091

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

7092

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

7093

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

7094

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

7095

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

7096

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

7097

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

7098

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

7099

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

7100

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