6.181 Problems 18001 to 18100

Table 6.361: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18001

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

18002

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

18003

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

18004

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

18005

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

18006

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

18007

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

18008

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

18009

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

18010

\[ {} {\mathrm e}^{y^{\prime }} = 1 \]

18011

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

18012

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

18013

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

18014

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

18015

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

18016

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

18017

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

18018

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

18019

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

18020

\[ {} {\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \]

18021

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

18022

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

18023

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

18024

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

18025

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

18026

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

18027

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

18028

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

18029

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

18030

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

18031

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

18032

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

18033

\[ {} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

18034

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

18035

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

18036

\[ {} 2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

18037

\[ {} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

18038

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

18039

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

18040

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

18041

\[ {} 4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

18042

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

18043

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

18044

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

18045

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

18046

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

18047

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

18048

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

18049

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

18050

\[ {} y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \]

18051

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

18052

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

18053

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

18054

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

18055

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

18056

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

18057

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

18058

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

18059

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

18060

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

18061

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

18062

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

18063

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

18064

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

18065

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

18066

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

18067

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

18068

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

18069

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

18070

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

18071

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

18072

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

18073

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

18074

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

18075

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

18076

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

18077

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

18078

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

18079

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

18080

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

18081

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

18082

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

18083

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

18084

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

18085

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

18086

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

18087

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

18088

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

18089

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

18090

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

18091

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

18092

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

18093

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

18094

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

18095

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

18096

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

18097

\[ {} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \]

18098

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

18099

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

18100

\[ {} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]