5.3.37 Problems 3601 to 3700

Table 5.119: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

12034

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

12035

\[ {} y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \]

12037

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

12038

\[ {} y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \]

12039

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

12040

\[ {} y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \]

12041

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

12042

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

12043

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

12044

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

12045

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

12046

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

12047

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

12049

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

12051

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

12052

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

12053

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

12055

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

12056

\[ {} y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \]

12057

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

12063

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

12066

\[ {} y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \]

12067

\[ {} y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \]

12070

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

12072

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

12073

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

12075

\[ {} y^{\prime } = \frac {-3 x^{2} y+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}} \]

12077

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

12078

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

12079

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

12080

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

12081

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

12082

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

12083

\[ {} y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \]

12084

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

12085

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

12086

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

12087

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

12088

\[ {} y^{\prime } = \frac {2 x^{2} \cosh \left (\frac {1}{x -1}\right )-2 x \cosh \left (\frac {1}{x -1}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (x -1\right ) \cosh \left (\frac {1}{x -1}\right )} \]

12089

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

12090

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

12091

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

12092

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

12093

\[ {} y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \]

12094

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

12095

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

12096

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

12097

\[ {} y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \]

12098

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

12099

\[ {} y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \]

12100

\[ {} y^{\prime } = \frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \]

12101

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

12102

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

12103

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

12104

\[ {} y^{\prime } = -\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \]

12106

\[ {} y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \]

12108

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

12109

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

12110

\[ {} y^{\prime } = \frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \]

12112

\[ {} y^{\prime } = \frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \]

12113

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

12116

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

12118

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

12120

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

12121

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

12122

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

12123

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

12124

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

12126

\[ {} y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \]

12127

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

12128

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

12129

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

12130

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

12131

\[ {} y^{\prime } = \frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (1+x \right )} \]

12132

\[ {} y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \]

12133

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

12134

\[ {} y^{\prime } = \frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{{7}/{2}}+100 x}{25 x} \]

12137

\[ {} y^{\prime } = \frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \]

12138

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

12139

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

12140

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

12141

\[ {} y^{\prime } = \frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \]

12142

\[ {} y^{\prime } = \frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \]

12143

\[ {} y^{\prime } = \frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \]

12144

\[ {} y^{\prime } = \frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \]

12145

\[ {} y^{\prime } = -\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \]

12146

\[ {} y^{\prime } = \frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \]

12147

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

12148

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

12150

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

12151

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

12152

\[ {} y^{\prime } = -\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \]

12153

\[ {} y^{\prime } = -\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \]

12154

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

12155

\[ {} y^{\prime } = -\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \]

12156

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

12157

\[ {} y^{\prime } = -\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]

12158

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

12159

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

12160

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