2.17.91 Problems 9001 to 9100

Problem 9001

ODE	\[ \boxed {y^{\prime }-\frac {y^{3} {\mathrm e}^{-2 x b}}{y \,{\mathrm e}^{-x b}+1}=0} \]
program solution	\[ -\frac {\left (\ln \left (y^{2} {\mathrm e}^{-2 x b}-y \,{\mathrm e}^{-x b} b -b \right )+2 c_{1} -2 \ln \left (y\right )\right ) \sqrt {b +4}+2 \sqrt {b}\, \operatorname {arctanh}\left (\frac {b -2 y \,{\mathrm e}^{-x b}}{\sqrt {b +4}\, \sqrt {b}}\right )}{2 \sqrt {b +4}} = 0 \] Verified OK.
Maple solution	\[ -\frac {-2 \ln \left (y \left (x \right ) {\mathrm e}^{-b x}\right ) \sqrt {b \left (4+b \right )}+\left (-2 b x +\ln \left (-b y \left (x \right ) {\mathrm e}^{-b x}+y \left (x \right )^{2} {\mathrm e}^{-2 b x}-b \right )+2 c_{1} \right ) \sqrt {b \left (4+b \right )}+2 b \,\operatorname {arctanh}\left (\frac {-2 y \left (x \right ) {\mathrm e}^{-b x}+b}{\sqrt {b \left (4+b \right )}}\right )}{2 \sqrt {b \left (4+b \right )}} = 0 \]

Problem 9002

ODE	\[ \boxed {y^{\prime }-\frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1}=0} \]
program solution	\[ \frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {2 \,{\mathrm e}^{-x} \sqrt {5}\, y}{5}-\frac {\sqrt {5}}{5}\right )}{5}+\ln \left (y\right )-\frac {\ln \left ({\mathrm e}^{2 x}+y \,{\mathrm e}^{x}-y^{2}\right )}{2} = -x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 \sqrt {5}\, \operatorname {arctanh}\left (\frac {\sqrt {5}\, \left (2 \,{\mathrm e}^{-x +\textit {\_Z}}-1\right )}{5}\right )-5 \ln \left ({\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x}\right )-10 c_{1} +10 \textit {\_Z} +10 x \right )} \]

Problem 9003

ODE	\[ \boxed {y^{\prime }-\frac {\left (-2 y^{\frac {3}{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}}=0} \]
program solution
Maple solution	\[ \frac {\left (3 \,{\mathrm e}^{2 x -\frac {3 \,{\mathrm e}^{x}}{2}-\frac {9 \,{\mathrm e}^{2 x}}{8}}+3 c_{1} {\mathrm e}^{2 x +\frac {3 \,{\mathrm e}^{x}}{2}-\frac {9 \,{\mathrm e}^{2 x}}{8}}+2 \left (1-y \left (x \right )^{\frac {3}{2}}\right ) {\mathrm e}^{x -\frac {3 \,{\mathrm e}^{x}}{2}-\frac {9 \,{\mathrm e}^{2 x}}{8}}+2 c_{1} \left (-1-y \left (x \right )^{\frac {3}{2}}\right ) {\mathrm e}^{x +\frac {3 \,{\mathrm e}^{x}}{2}-\frac {9 \,{\mathrm e}^{2 x}}{8}}\right ) {\mathrm e}^{-x -\frac {3 \,{\mathrm e}^{x}}{2}+\frac {9 \,{\mathrm e}^{2 x}}{8}}}{-2 y \left (x \right )^{\frac {3}{2}}+3 \,{\mathrm e}^{x}-2} = 0 \]

Problem 9004

ODE	\[ \boxed {y^{\prime }-\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2}=0} \]
program solution
Maple solution	\[ -\frac {i \ln \left (-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )+1\right )}{4}-\frac {\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}}{2}+\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}\right )}{2}-\frac {i x^{2}}{2}-c_{1} = 0 \]

Problem 9005

ODE	\[ \boxed {y^{\prime }-\frac {\left (y^{2} x +1\right )^{2}}{y x^{4}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, {\mathrm e}^{\frac {\sqrt {2}\, x +1}{x^{2}}} \sqrt {-\left ({\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \right ) x \left (\left (2-\sqrt {2}\, x \right ) {\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \left (\sqrt {2}\, x +2\right )\right ) {\mathrm e}^{-\frac {2}{x^{2}}} {\mathrm e}^{-\frac {2 \sqrt {2}}{x}}}}{2 x \left ({\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \right )} \\ y \left (x \right ) &= \frac {\sqrt {2}\, {\mathrm e}^{\frac {\sqrt {2}\, x +1}{x^{2}}} \sqrt {-\left ({\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \right ) x \left (\left (2-\sqrt {2}\, x \right ) {\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \left (\sqrt {2}\, x +2\right )\right ) {\mathrm e}^{-\frac {2}{x^{2}}} {\mathrm e}^{-\frac {2 \sqrt {2}}{x}}}}{2 x \left ({\mathrm e}^{\frac {2 \sqrt {2}}{x}}+c_{1} \right )} \\ \end{align*}

Problem 9006

ODE	\[ \boxed {y^{\prime }-\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}}=0} \]
program solution
Maple solution	\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {-9 x^{4}+4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}-c_{1} = 0 \]

Problem 9007

ODE	\[ \boxed {y^{\prime }-\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x}=0} \]
program solution	\[ -\frac {x \left (\cos \left (2 y\right ) x^{2}+x^{2}-3 \sin \left (2 y\right )\right )}{3 \cos \left (2 y\right )+3} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arctan \left (\frac {x^{3}+6 c_{1}}{3 x}\right ) \]

Problem 9008

ODE	\[ \boxed {y^{\prime }+\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 x +2}=0} \]
program solution	\[ y = \ln \left (x +1\right )^{2}+4 \ln \left (x +1\right ) c_{1} +4 c_{1}^{2}-\frac {x^{2}}{4}+x \] Verified OK.
Maple solution	\[ c_{1} +2 \ln \left (x +1\right )-1-\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0 \]

Problem 9009

ODE	\[ \boxed {y^{\prime }-\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-y^{2} x}{x}=0} \]
program solution	\[ y = \frac {x \sqrt {-a}\, \left (c_{3} \cos \left (\frac {\left (\left (6 x -6\right ) {\mathrm e}^{x}+2 x^{3}+3 x^{2}\right ) \sqrt {-a}}{6}\right )-\sin \left (\frac {\left (\left (6 x -6\right ) {\mathrm e}^{x}+2 x^{3}+3 x^{2}\right ) \sqrt {-a}}{6}\right )\right )}{c_{3} \sin \left (\frac {\left (\left (6 x -6\right ) {\mathrm e}^{x}+2 x^{3}+3 x^{2}\right ) \sqrt {-a}}{6}\right )+\cos \left (\frac {\left (\left (6 x -6\right ) {\mathrm e}^{x}+2 x^{3}+3 x^{2}\right ) \sqrt {-a}}{6}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tanh \left (\frac {\left (\left (6 x -6\right ) {\mathrm e}^{x}+2 x^{3}+3 x^{2}+6 c_{1} \right ) \sqrt {a}}{6}\right ) \sqrt {a}\, x \]

Problem 9010

ODE	\[ \boxed {y^{\prime }-\frac {x +1+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3} \left (x +1\right )}=0} \]
program solution
Maple solution	\[ \frac {3 x^{5}-4 x^{4}+6 x^{3}+12 \ln \left (x +1\right ) x +6 c_{1} x -12 x^{2}-6 \sqrt {4 x^{2} y \left (x \right )+1}}{6 x} = 0 \]

Problem 9011

ODE	\[ \boxed {y^{\prime }-\frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-y^{2} x^{2}-y^{2} x}{x}=0} \]
program solution	\[ y = \frac {i \sqrt {-x^{2} \left (\ln \left (x +1\right )+x +1\right )^{2} a}\, \left (c_{3} {\mathrm e}^{i \left (\int \sqrt {-x^{2} \left (\ln \left (x +1\right )+x +1\right )^{2} a}d x \right )}-{\mathrm e}^{-i \left (\int \sqrt {-x^{2} \left (\ln \left (x +1\right )+x +1\right )^{2} a}d x \right )}\right )}{\left (\ln \left (x +1\right )+x +1\right ) \left (c_{3} {\mathrm e}^{i \left (\int \sqrt {-x^{2} \left (\ln \left (x +1\right )+x +1\right )^{2} a}d x \right )}+{\mathrm e}^{-i \left (\int \sqrt {-x^{2} \left (\ln \left (x +1\right )+x +1\right )^{2} a}d x \right )}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tanh \left (\frac {\sqrt {a}\, \left (6 \ln \left (x +1\right ) x^{2}+4 x^{3}+3 x^{2}-6 \ln \left (x +1\right )+12 c_{1} +6 x +9\right )}{12}\right ) \sqrt {a}\, x \]

Problem 9012

ODE	\[ \boxed {y^{\prime }-\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} -x^{3}+\frac {3 x^{2}}{2}-3 x +3 \ln \left (x +1\right )-\frac {1}{2}-\sqrt {x^{3}-6 y \left (x \right )} = 0 \]

Problem 9013

ODE	\[ \boxed {y^{\prime }-\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 y^{2} x}{x}=0} \]
program solution	\[ y = \frac {x \left (-c_{3} \cos \left (\frac {\sqrt {7}\, x^{2} \left (6 \ln \left (x \right )+3+4 x \right )}{12}\right )+\sin \left (\frac {\sqrt {7}\, x^{2} \left (6 \ln \left (x \right )+3+4 x \right )}{12}\right )\right ) \sqrt {7}}{7 c_{3} \sin \left (\frac {\sqrt {7}\, x^{2} \left (6 \ln \left (x \right )+3+4 x \right )}{12}\right )+7 \cos \left (\frac {\sqrt {7}\, x^{2} \left (6 \ln \left (x \right )+3+4 x \right )}{12}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (6 x^{2} \ln \left (x \right )+4 x^{3}+3 x^{2}+12 c_{1} \right ) \sqrt {7}}{12}\right ) x \sqrt {7}}{7} \]

Problem 9014

ODE	\[ \boxed {y^{\prime }-\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 \left (x +1\right )}=0} \]
program solution	\[ y = -\ln \left (x +1\right )^{2}+4 \ln \left (x +1\right ) c_{1} -4 c_{1}^{2}+\frac {x^{2}}{4}+\frac {x}{2}+\frac {1}{4} \] Verified OK.
Maple solution	\[ c_{1} -2 \ln \left (x +1\right )-\frac {1}{2}-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0 \]

Problem 9015

ODE	\[ \boxed {y^{\prime }-\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+y^{2} a \,x^{2}+y^{2} a x}{x}=0} \]
program solution	\[ y = \frac {\left (\ln \left (\frac {1}{x}\right )+x +1\right ) x^{2} b \left (-c_{3} \cos \left (\frac {\sqrt {a \,x^{2} \left (\ln \left (\frac {1}{x}\right )+x +1\right )^{2} b}\, x \left (6 \ln \left (\frac {1}{x}\right )+9+4 x \right )}{12 \ln \left (\frac {1}{x}\right )+12 x +12}\right )+\sin \left (\frac {\sqrt {a \,x^{2} \left (\ln \left (\frac {1}{x}\right )+x +1\right )^{2} b}\, x \left (6 \ln \left (\frac {1}{x}\right )+9+4 x \right )}{12 \ln \left (\frac {1}{x}\right )+12 x +12}\right )\right )}{\left (c_{3} \sin \left (\frac {\sqrt {a \,x^{2} \left (\ln \left (\frac {1}{x}\right )+x +1\right )^{2} b}\, x \left (6 \ln \left (\frac {1}{x}\right )+9+4 x \right )}{12 \ln \left (\frac {1}{x}\right )+12 x +12}\right )+\cos \left (\frac {\sqrt {a \,x^{2} \left (\ln \left (\frac {1}{x}\right )+x +1\right )^{2} b}\, x \left (6 \ln \left (\frac {1}{x}\right )+9+4 x \right )}{12 \ln \left (\frac {1}{x}\right )+12 x +12}\right )\right ) \sqrt {a \,x^{2} \left (\ln \left (\frac {1}{x}\right )+x +1\right )^{2} b}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (6 x^{2} \ln \left (\frac {1}{x}\right )+4 x^{3}+9 x^{2}+12 c_{1} \right ) \sqrt {a b}}{12}\right ) x \sqrt {a b}}{a} \]

Problem 9016

ODE	\[ \boxed {y^{\prime }-\frac {2 a}{x \left (-x y+2 y^{2} a x -8 a^{2}\right )}=0} \]
program solution	\[ \frac {-4 y a +\ln \left (y^{2} x -4 a \right )}{8 a^{2}} = \frac {\ln \left (x \right )}{8 a^{2}}+c_{1} \] Verified OK.
Maple solution	\[ \frac {\left (-x y \left (x \right )^{2}+4 a \right ) {\mathrm e}^{-4 a y \left (x \right )}+c_{1} x}{x} = 0 \]

Problem 9017

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x}=0} \]
program solution	\[ y = -\frac {\left (x \left (x +1\right )\right )^{-\frac {x^{3}}{3}} {\mathrm e}^{\frac {2}{9} x^{3}-\frac {1}{6} x^{2}+\frac {1}{3} x}}{x \left (x +1\right )^{\frac {1}{3}} \left (c_{3} +\int \frac {\ln \left (x \left (x +1\right )\right ) x^{2} \left (x \left (x +1\right )\right )^{-\frac {x^{3}}{3}} {\mathrm e}^{\frac {2}{9} x^{3}-\frac {1}{6} x^{2}+\frac {1}{3} x}}{\left (x +1\right )^{\frac {1}{3}}}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{x \left (\left (x \left (x +1\right )\right )^{\frac {x^{3}}{3}} c_{1} \left (x +1\right )^{\frac {1}{3}} {\mathrm e}^{-\frac {2}{9} x^{3}+\frac {1}{6} x^{2}-\frac {1}{3} x}+1\right )} \]

Problem 9018

ODE	\[ \boxed {y^{\prime }-\frac {y+\sqrt {y^{2}+x^{2}}\, x^{2}}{x}=0} \]
program solution
Maple solution	\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{2}}{2}-\ln \left (x \right )-c_{1} = 0 \]

Problem 9019

ODE	\[ \boxed {y^{\prime }-\frac {y+\ln \left (\left (x -1\right ) \left (x +1\right )\right ) x^{3}+7 \ln \left (\left (x -1\right ) \left (x +1\right )\right ) x y^{2}}{x}=0} \]
program solution	\[ y = -\frac {\sqrt {7}\, \left (c_{3} \cos \left (\frac {\sqrt {7}\, \left (\ln \left (x^{2}-1\right )-1\right ) \left (x^{2}-1\right )}{2}\right )-\sin \left (\frac {\sqrt {7}\, \left (\ln \left (x^{2}-1\right )-1\right ) \left (x^{2}-1\right )}{2}\right )\right ) x}{7 c_{3} \sin \left (\frac {\sqrt {7}\, \left (\ln \left (x^{2}-1\right )-1\right ) \left (x^{2}-1\right )}{2}\right )+7 \cos \left (\frac {\sqrt {7}\, \left (\ln \left (x^{2}-1\right )-1\right ) \left (x^{2}-1\right )}{2}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (x^{2} \ln \left (x^{2}-1\right )-x^{2}-\ln \left (x^{2}-1\right )+2 c_{1} +1\right ) \sqrt {7}}{2}\right ) x \sqrt {7}}{7} \]

Problem 9020

ODE	\[ \boxed {y^{\prime }-\frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \left (\cot \left (\operatorname {RootOf}\left (-2 x^{2}-\ln \left (2\right )+\ln \left (5\right )-\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (-1+\tan \left (\textit {\_Z} \right )\right )+6 c_{1} -2 \textit {\_Z} \right )\right )-1\right ) {\mathrm e}^{-x^{2}} \]

Problem 9021

ODE	\[ \boxed {y^{\prime }-\frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x}=0} \]
program solution	\[ y = -\frac {x \left (\cosh \left (x -1+\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}\right ) c_{3} +\sinh \left (x -1+\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}\right )\right )}{\sinh \left (x -1+\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}\right ) c_{3} +\cosh \left (x -1+\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\tanh \left (\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}+c_{1} +x -1\right ) x \]

Problem 9022

ODE	\[ \boxed {y^{\prime }-\frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x}=0} \]
program solution	\[ y = \frac {\left (-c_{3} \cos \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )\right )+\sin \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )\right )\right ) x}{c_{3} \sin \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )\right )+\cos \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )+c_{1} \right ) x \]

Problem 9023

ODE	\[ \boxed {y^{\prime }-\frac {x y-y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x}=0} \]
program solution	\[ y = -i \tan \left (i \operatorname {expIntegral}_{1}\left (1-x \right ) {\mathrm e}^{2}-i {\mathrm e}^{x +1}+c_{3} \right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\tanh \left ({\mathrm e}^{x +1}-{\mathrm e}^{2} \operatorname {expIntegral}_{1}\left (1-x \right )+c_{1} \right ) x \]

Problem 9024

ODE	\[ \boxed {y^{\prime }-\frac {-x^{2}+1+4 \sqrt {x^{2}-2 x +1+8 y}\, x^{3}}{4 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} +\frac {4 x^{3}}{3}-2 x^{2}-4 \ln \left (x +1\right )+4 x -\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0 \]

Problem 9025

ODE	\[ \boxed {y^{\prime }-\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x}=0} \]
program solution	\[ -\frac {x \left (\cos \left (2 y\right ) x^{3}+x^{3}-4 \sin \left (2 y\right )\right )}{4 \cos \left (2 y\right )+4} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arctan \left (\frac {x^{4}+8 c_{1}}{4 x}\right ) \]

Problem 9026

ODE	\[ \boxed {y^{\prime }-\frac {y+x^{3} \sqrt {y^{2}+x^{2}}}{x}=0} \]
program solution
Maple solution	\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{3}}{3}-\ln \left (x \right )-c_{1} = 0 \]

Problem 9027

ODE	\[ \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{-2 x b}+{\mathrm e}^{-3 x b} y^{3}\right ) {\mathrm e}^{x b}=0} \]
program solution	\[ x = \int _{}^{y \,{\mathrm e}^{-x b}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} b +1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} b +1}d \textit {\_a} +c_{1} \right ) {\mathrm e}^{b x} \]

Problem 9028

ODE	\[ \boxed {y^{\prime }-\frac {x +1+2 \sqrt {1+4 x^{2} y}\, x^{3}}{2 x^{3} \left (x +1\right )}=0} \]
program solution
Maple solution	\[ \frac {-2 \ln \left (x +1\right ) x +c_{1} x +2 x^{2}-\sqrt {4 x^{2} y \left (x \right )+1}}{x} = 0 \]

Problem 9029

ODE	\[ \boxed {y^{\prime }-\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+y^{2} x^{2}+y^{2} x}{\ln \left (x -1\right ) x}=0} \]
program solution	\[ y = \frac {\left (c_{3} \cos \left (\operatorname {expIntegral}_{1}\left (-3 \ln \left (x -1\right )\right )+3 \,\operatorname {expIntegral}_{1}\left (-2 \ln \left (x -1\right )\right )+2 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x -1\right )\right )\right )-\sin \left (\operatorname {expIntegral}_{1}\left (-3 \ln \left (x -1\right )\right )+3 \,\operatorname {expIntegral}_{1}\left (-2 \ln \left (x -1\right )\right )+2 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x -1\right )\right )\right )\right ) x}{c_{3} \sin \left (\operatorname {expIntegral}_{1}\left (-3 \ln \left (x -1\right )\right )+3 \,\operatorname {expIntegral}_{1}\left (-2 \ln \left (x -1\right )\right )+2 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x -1\right )\right )\right )+\cos \left (\operatorname {expIntegral}_{1}\left (-3 \ln \left (x -1\right )\right )+3 \,\operatorname {expIntegral}_{1}\left (-2 \ln \left (x -1\right )\right )+2 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x -1\right )\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (-\operatorname {expIntegral}_{1}\left (-3 \ln \left (x -1\right )\right )-3 \,\operatorname {expIntegral}_{1}\left (-2 \ln \left (x -1\right )\right )-2 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x -1\right )\right )+c_{1} \right ) x \]

Problem 9030

ODE	\[ \boxed {y^{\prime }-\frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x}=0} \]
program solution	\[ y = \frac {x \sqrt {7}\, \tan \left (\sqrt {7}\, {\mathrm e} \left (\int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x \right )+c_{3} \right )}{7} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tan \left (\left ({\mathrm e} \left (\int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x \right )+c_{1} \right ) \sqrt {7}\right ) x \sqrt {7}}{7} \]

Problem 9031

ODE	\[ \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+{\mathrm e}^{-2 x} y^{3}\right ) {\mathrm e}^{\frac {2 x}{3}}=0} \]
program solution	\[ \frac {2 x}{3} = \int _{}^{y \,{\mathrm e}^{-\frac {2 x}{3}}}\frac {2}{3 \textit {\_a}^{3}+3 \textit {\_a}^{2}-2 \textit {\_a} +3}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-x +3 \left (\int _{}^{\textit {\_Z}}\frac {1}{3 \textit {\_a}^{3}+3 \textit {\_a}^{2}-2 \textit {\_a} +3}d \textit {\_a} \right )+c_{1} \right ) {\mathrm e}^{\frac {2 x}{3}} \]

Problem 9032

ODE	\[ \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x}=0} \]
program solution	\[ x = \int _{}^{y \,{\mathrm e}^{-x}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} +1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} +1}d \textit {\_a} +c_{1} \right ) {\mathrm e}^{x} \]

Problem 9033

ODE	\[ \boxed {y^{\prime }-\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} +\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 \ln \left (x +1\right )}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0 \]

Problem 9034

ODE	\[ \boxed {y^{\prime }-\frac {1}{x \left (y^{2} x +1+x \right ) y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {x \left (2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x -1}{2 x}}}{2}\right ) x +x -1\right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x -1}{2 x}}}{2}\right ) x +x -1\right )}}{x} \\ \end{align*}

Problem 9035

ODE	\[ \boxed {y^{\prime }-\frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y x^{2} \ln \left (x \right )-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1}=0} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {-2 x \left ({\mathrm e}^{x}-\frac {{\mathrm e}^{2 x}}{2}-\frac {1}{2}\right ) \left (\ln \left (x \right )+1\right ) \textit {\_Y}^{\prime \prime }\left (x \right )+\textit {\_Y}^{\prime }\left (x \right ) \left (x \ln \left (x \right )+x -1\right ) {\mathrm e}^{2 x}+\left (2 x^{3} \left ({\mathrm e}^{x}-1\right ) \ln \left (x \right )^{2}+\left (\left (4 x^{3}-x \right ) {\mathrm e}^{x}-4 x^{3}\right ) \ln \left (x \right )+\left (2 x^{3}-x +2\right ) {\mathrm e}^{x}-2 x^{3}-1\right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y} \left (x \right ) x \left (\ln \left (x \right )+1\right )^{2} \left (\left (x^{4}-1\right ) \ln \left (x \right )+x^{4}+2 x \,{\mathrm e}^{x}-2 x -1\right )}{x \left ({\mathrm e}^{x}-1\right )^{2} \left (\ln \left (x \right )+1\right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) \left ({\mathrm e}^{x}-1\right )}{\left (\ln \left (x \right )+1\right ) \operatorname {DESol}\left (\left \{\frac {-2 x \left ({\mathrm e}^{x}-\frac {{\mathrm e}^{2 x}}{2}-\frac {1}{2}\right ) \left (\ln \left (x \right )+1\right ) \textit {\_Y}^{\prime \prime }\left (x \right )+\textit {\_Y}^{\prime }\left (x \right ) \left (x \ln \left (x \right )+x -1\right ) {\mathrm e}^{2 x}+\left (2 x^{3} \left ({\mathrm e}^{x}-1\right ) \ln \left (x \right )^{2}+\left (\left (4 x^{3}-x \right ) {\mathrm e}^{x}-4 x^{3}\right ) \ln \left (x \right )+\left (2 x^{3}-x +2\right ) {\mathrm e}^{x}-2 x^{3}-1\right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y} \left (x \right ) x \left (\ln \left (x \right )+1\right )^{2} \left (\left (x^{4}-1\right ) \ln \left (x \right )+x^{4}+2 x \,{\mathrm e}^{x}-2 x -1\right )}{x \left ({\mathrm e}^{x}-1\right )^{2} \left (\ln \left (x \right )+1\right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-x^{2} {\mathrm e}^{2 \left (\int \frac {\ln \left (x \right )+1}{{\mathrm e}^{x}-1}d x \right )}+c_{1} x^{2}+{\mathrm e}^{2 \left (\int \frac {\ln \left (x \right )+1}{{\mathrm e}^{x}-1}d x \right )}+c_{1}}{-{\mathrm e}^{2 \left (\int \frac {\ln \left (x \right )+1}{{\mathrm e}^{x}-1}d x \right )}+c_{1}} \]

Problem 9036

ODE	\[ \boxed {y^{\prime }-\frac {-y \,{\mathrm e}^{x}+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-y^{2} x}{\left (-{\mathrm e}^{x}+x \right ) x}=0} \]
program solution	\[ y = -\frac {i \left (c_{3} {\mathrm e}^{i \left (\int \frac {x \left (\ln \left (x \right )+1\right )}{{\mathrm e}^{x}-x}d x \right )}-{\mathrm e}^{-i \left (\int \frac {x \left (\ln \left (x \right )+1\right )}{{\mathrm e}^{x}-x}d x \right )}\right ) x}{c_{3} {\mathrm e}^{i \left (\int \frac {x \left (\ln \left (x \right )+1\right )}{{\mathrm e}^{x}-x}d x \right )}+{\mathrm e}^{-i \left (\int \frac {x \left (\ln \left (x \right )+1\right )}{{\mathrm e}^{x}-x}d x \right )}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (\int \frac {x \ln \left (x \right )}{{\mathrm e}^{x}-x}d x +\int \frac {x}{{\mathrm e}^{x}-x}d x +c_{1} \right ) x \]

Problem 9037

ODE	\[ \boxed {y^{\prime }-\frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x}=0} \]
program solution	\[ y = -\frac {{\mathrm e}^{-\left (\int \frac {\ln \left (x \right )^{2} x +\left (2 x^{2}+x \right ) \ln \left (x \right )+x^{3}+1}{x \left (\ln \left (x \right )+x \right ) \left (x -1\right )}d x \right )} \left (x -1\right )}{x \left (\ln \left (x \right )+x \right ) \left (c_{3} +\int {\mathrm e}^{-\left (\int \frac {\ln \left (x \right )^{2} x +\left (2 x^{2}+x \right ) \ln \left (x \right )+x^{3}+1}{x \left (\ln \left (x \right )+x \right ) \left (x -1\right )}d x \right )}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {dilog}\left (x \right )-x}}{x \left (-\left (\int \frac {{\mathrm e}^{\operatorname {dilog}\left (x \right )-x} \left (\ln \left (x \right )+x \right )}{\left (x -1\right )^{2}}d x \right )+c_{1} \right ) \left (x -1\right )} \]

Problem 9038

ODE	\[ \boxed {y^{\prime }-\frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x}=0} \]
program solution	\[ y = -\frac {i x \sqrt {a b}\, \left (c_{3} {\mathrm e}^{2 i \sqrt {a b}\, \left (\int \frac {x^{3}}{x \ln \left (x \right )-1}d x \right )}-{\mathrm e}^{-2 i \sqrt {a b}\, \left (\int \frac {x^{3}}{x \ln \left (x \right )-1}d x \right )}\right )}{a \left (c_{3} {\mathrm e}^{2 i \sqrt {a b}\, \left (\int \frac {x^{3}}{x \ln \left (x \right )-1}d x \right )}+{\mathrm e}^{-2 i \sqrt {a b}\, \left (\int \frac {x^{3}}{x \ln \left (x \right )-1}d x \right )}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tan \left (2 \sqrt {a b}\, \left (\int \frac {x^{3}}{x \ln \left (x \right )-1}d x +c_{1} \right )\right ) x \sqrt {a b}}{a} \]

Problem 9039

ODE	\[ \boxed {y^{\prime }-\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}=0} \]
program solution	\[ y = {\mathrm e}^{\frac {x^{4}}{3}+\frac {x^{3}}{2}+x \ln \left (x \right )+c_{1} x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{x} {\mathrm e}^{c_{1} x +\frac {1}{2} x^{3}+\frac {1}{3} x^{4}} \]

Problem 9040

ODE	\[ \boxed {y^{\prime }+\frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8}=0} \]
program solution	\[ \ln \left (x \right ) = \int _{}^{-\ln \left (x \right )-\operatorname {arctanh}\left (y\right )}-\frac {8 \,{\mathrm e}^{2 \textit {\_a}}}{i \pi +8 \,{\mathrm e}^{2 \textit {\_a}}+2 \textit {\_a}}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= {\mathrm e}^{\operatorname {RootOf}\left (-x^{2} {\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}-2}{x^{2}}\right )+\textit {\_Z} \,x^{2} {\mathrm e}^{\textit {\_Z}}+8 \,{\mathrm e}^{\textit {\_Z}}-16\right )}-1 \\ -\left (\int _{\textit {\_b}}^{y \left (x \right )}-\frac {1}{2 \left (\textit {\_a} +1\right ) \left (-\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} -1\right )}{2}+\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )}{2}+x^{2} \left (\textit {\_a} +1\right ) \ln \left (x \right )+4 \textit {\_a} -4\right )}d \textit {\_a} \right )+\frac {\ln \left (x \right )}{8}-c_{1} &= 0 \\ \end{align*}

Problem 9041

ODE	\[ \boxed {y^{\prime }-\frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16}=0} \]
program solution	\[ \ln \left (x \right ) = \int _{}^{-\ln \left (x \right )-\operatorname {arctanh}\left (y\right )}\frac {16 \,{\mathrm e}^{2 \textit {\_a}}}{-4 i \pi \textit {\_a} +\pi ^{2}-16 \,{\mathrm e}^{2 \textit {\_a}}-4 \textit {\_a}^{2}}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= {\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}} \textit {\_Z}^{2}-2 x^{2} {\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}-2}{x^{2}}\right ) \textit {\_Z} +4 \ln \left (x \right )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}-4 \ln \left (x \right ) \ln \left ({\mathrm e}^{\textit {\_Z}}-2\right ) x^{2} {\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}-16 \,{\mathrm e}^{\textit {\_Z}}+32\right )}-1 \\ \int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{4 \left (\textit {\_a} +1\right ) \left (\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} -1\right )^{2}}{4}-\left (\ln \left (x \right )+\frac {\ln \left (\textit {\_a} +1\right )}{2}\right ) \left (\textit {\_a} +1\right ) x^{2} \ln \left (\textit {\_a} -1\right )+\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )^{2}}{4}+x^{2} \left (\textit {\_a} +1\right ) \ln \left (x \right ) \ln \left (\textit {\_a} +1\right )+x^{2} \left (\textit {\_a} +1\right ) \ln \left (x \right )^{2}-4 \textit {\_a} +4\right )}d \textit {\_a} -\frac {\ln \left (x \right )}{16}-c_{1} &= 0 \\ \end{align*}

Problem 9042

ODE	\[ \boxed {y^{\prime }-\frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y}=0} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 9043

ODE	\[ \boxed {y^{\prime }-\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y}=0} \]
program solution
Maple solution	\[ -\sqrt {4 a x -y \left (x \right )^{2}}-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-c_{1} = 0 \]

Problem 9044

ODE	\[ \boxed {y^{\prime }-\frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 y^{2} x +2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}=0} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {\left (x^{2} \textit {\_Y}^{\prime \prime }\left (x \right )-\textit {\_Y}^{\prime }\left (x \right ) \left (x +1\right )\right ) {\mathrm e}^{\frac {2}{x}}+\left (-2 x^{2} \ln \left (x \right ) \textit {\_Y}^{\prime \prime }\left (x \right )+\left (\left (2 x +1\right ) \ln \left (x \right )+4 x^{4}-x \right ) \textit {\_Y}^{\prime }\left (x \right )+2 x^{3} \textit {\_Y} \left (x \right )\right ) {\mathrm e}^{\frac {1}{x}}+4 \left (\frac {x \ln \left (x \right )^{2} \textit {\_Y}^{\prime \prime }\left (x \right )}{4}-\ln \left (x \right ) \left (x^{3}+\frac {\ln \left (x \right )}{4}-\frac {1}{4}\right ) \textit {\_Y}^{\prime }\left (x \right )+x^{2} \textit {\_Y} \left (x \right ) \left (x^{3}+x -\frac {\ln \left (x \right )}{2}\right )\right ) x}{x^{2} \left (\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}\right )^{2}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) \left (\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}\right )}{2 x \operatorname {DESol}\left (\left \{\frac {\left (x^{2} \textit {\_Y}^{\prime \prime }\left (x \right )-\textit {\_Y}^{\prime }\left (x \right ) \left (x +1\right )\right ) {\mathrm e}^{\frac {2}{x}}+\left (-2 x^{2} \ln \left (x \right ) \textit {\_Y}^{\prime \prime }\left (x \right )+\left (\left (2 x +1\right ) \ln \left (x \right )+4 x^{4}-x \right ) \textit {\_Y}^{\prime }\left (x \right )+2 x^{3} \textit {\_Y} \left (x \right )\right ) {\mathrm e}^{\frac {1}{x}}+4 \left (\frac {x \ln \left (x \right )^{2} \textit {\_Y}^{\prime \prime }\left (x \right )}{4}-\ln \left (x \right ) \left (x^{3}+\frac {\ln \left (x \right )}{4}-\frac {1}{4}\right ) \textit {\_Y}^{\prime }\left (x \right )+x^{2} \textit {\_Y} \left (x \right ) \left (x^{3}+x -\frac {\ln \left (x \right )}{2}\right )\right ) x}{x^{2} \left (\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}\right )^{2}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x +\tan \left (2 c_{1} +2 \left (\int \frac {x}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}d x \right )\right ) \]

Problem 9045

ODE	\[ \boxed {y^{\prime }+\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{-x} c_{1} -\operatorname {expIntegral}_{1}\left (-x -1\right ) {\mathrm e}^{-x -1}} \]

Problem 9046

ODE	\[ \boxed {y^{\prime }-\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}\, x^{3}}{2 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} -\frac {2 x^{3}}{3}+x^{2}-2 x +2 \ln \left (x +1\right )-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0 \]

Problem 9047

ODE	\[ \boxed {y^{\prime }-\frac {-y a b +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-y a +b +a +x b -a \sqrt {x}\right )}=0} \]
program solution	\[ \frac {b \left (3 \ln \left (x^{\frac {3}{2}} a b -a \left (\left (y-1\right ) a -b \right ) \sqrt {x}+\left (-y^{2}+2 x +2 y-1\right ) a^{2}+2 b \left (y-1\right ) \left (x +1\right ) a -b^{2} \left (x +1\right )^{2}\right )-2 \,\operatorname {arctanh}\left (\frac {a \sqrt {x}+\left (2 y-2\right ) a -2 b \left (x +1\right )}{3 \sqrt {x}\, a}\right )\right )}{6 a} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-x^{\frac {3}{2}} a b +b^{2} x^{2}-a^{2} \sqrt {x}-b a \sqrt {x}-2 a^{2} x +2 a x b +2 b^{2} x +a^{2}+2 a b +b^{2}+{\mathrm e}^{\operatorname {RootOf}\left (-4 \,{\mathrm e}^{\textit {\_Z}}+9 \operatorname {sech}\left (-\frac {3 \textit {\_Z}}{2}+\frac {c_{1}}{2}\right )^{2} a^{2} x \right )}+\left (a \sqrt {x}-2 b x -2 a -2 b \right ) \textit {\_Z} +\textit {\_Z}^{2}\right )}{a} \]

Problem 9048

ODE	\[ \boxed {y^{\prime }+\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}=0} \]
program solution	\[ y = \frac {{\mathrm e}^{-\left (\int \frac {\left (x +1\right ) \ln \left (\frac {1}{x}\right )+\left (x^{2}+x \ln \left (x \right )-x -1\right ) {\mathrm e}^{x}-\left (\ln \left (x \right )+x \right ) \left (x^{2}+x \ln \left (x \right )-1\right )}{x \left (\ln \left (x \right )+x \right ) \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right )}d x \right )} \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right )}{x \left (\ln \left (x \right )+x \right ) \left (c_{3} +\int {\mathrm e}^{-\left (\int \frac {\left (x +1\right ) \ln \left (\frac {1}{x}\right )+\left (x^{2}+x \ln \left (x \right )-x -1\right ) {\mathrm e}^{x}-\left (\ln \left (x \right )+x \right ) \left (x^{2}+x \ln \left (x \right )-1\right )}{x \left (\ln \left (x \right )+x \right ) \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right )}d x \right )}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {x \ln \left (x \right )+x^{2}-{\mathrm e}^{x}+\ln \left (\frac {1}{x}\right )}{x \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right )}d x}}{\int \frac {{\mathrm e}^{\int \frac {x \ln \left (x \right )+x^{2}-{\mathrm e}^{x}+\ln \left (\frac {1}{x}\right )}{x \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right )}d x} x \left (\ln \left (x \right )+x \right )}{-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}}d x +c_{1}} \]

Problem 9049

ODE	\[ \boxed {y^{\prime }-\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} +\frac {2 x^{3}}{3}-x^{2}-2 \ln \left (x +1\right )+2 x -\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0 \]

Problem 9050

ODE	\[ \boxed {y^{\prime }-\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}=0} \]
program solution
Maple solution	\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\ln \left (x +1\right )-c_{1} = 0 \]

Problem 9051

ODE	\[ \boxed {y^{\prime }+\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}=0} \]
program solution	\[ y = \ln \left (x +1\right )^{2}+4 \ln \left (x +1\right ) c_{1} +4 c_{1}^{2}-\frac {a^{2}}{4}-\frac {a x}{2}-\frac {x^{2}}{4} \] Verified OK.
Maple solution	\[ c_{1} +\frac {a}{2}+2 \ln \left (x +1\right )-\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )} = 0 \]

Problem 9052

ODE	\[ \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x=0} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {11 \,{\mathrm e}^{-x^{2}} \operatorname {RootOf}\left (-5 x^{2}+20250 \left (\int _{}^{\textit {\_Z}}\frac {1}{121 \textit {\_a}^{3}+3375 \textit {\_a} -3375}d \textit {\_a} \right )+6 c_{1} \right )}{45}-\frac {{\mathrm e}^{-x^{2}}}{3} \]

Problem 9053

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}=0} \]
program solution	\[ y = -\frac {x^{-1+{\mathrm e}^{-x}} {\mathrm e}^{\operatorname {expIntegral}_{1}\left (x \right )} 2^{{\mathrm e}^{-x}}}{c_{3} +\int x^{{\mathrm e}^{-x}} 2^{{\mathrm e}^{-x}} {\mathrm e}^{-x +\operatorname {expIntegral}_{1}\left (x \right )} \left (\ln \left (2\right )+\ln \left (x \right )\right )d x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{x \left (1+2^{-{\mathrm e}^{-x}} x^{-{\mathrm e}^{-x}} {\mathrm e}^{-\operatorname {expIntegral}_{1}\left (x \right )} c_{1} \right )} \]

Problem 9054

ODE	\[ \boxed {y^{\prime }-\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}=0} \]
program solution
Maple solution	\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-c_{1} = 0 \]

Problem 9055

ODE	\[ \boxed {y^{\prime }-\frac {\left (18 x^{\frac {3}{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}=0} \]
program solution	\[ y = \frac {c_{3} x^{\frac {7}{2}}+x^{5}-9 \sqrt {x}}{\sqrt {x}\, \left (6 c_{3} +6 x^{\frac {3}{2}}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{3}}{6}-\frac {3}{2 x^{\frac {3}{2}}-3 c_{1}} \]

Problem 9056

ODE	\[ \boxed {y^{\prime }+\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}=0} \]
program solution	\[ \frac {\ln \left (4 y \ln \left (x \right )-3 y-2\right ) y-y \ln \left (y\right )-2}{2 y} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+2}{x^{4}}\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +2\right )}}{1+\left (2 \ln \left (x \right )-1\right ) {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+2}{x^{4}}\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +2\right )}} \]

Problem 9057

ODE	\[ \boxed {y^{\prime }-\frac {2 a}{y+2 y^{4} a -16 a^{2} x y^{2}+32 a^{3} x^{2}}=0} \]
program solution	\[ \frac {16 y a^{2} x -4 y^{3} a +1}{32 a^{3} x -8 y^{2} a^{2}} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {{\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}}{6 a}+\frac {8 a^{2} \left (a \,c_{1}^{2}+3 x \right )}{3 {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}}+\frac {2 c_{1} a}{3} \\ y \left (x \right ) &= \frac {\frac {\left (-i \sqrt {3}-1\right ) {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {2}{3}}}{12}+\frac {4 a^{2} \left (\frac {c_{1} {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}}{2}+\left (a \,c_{1}^{2}+3 x \right ) a \left (i \sqrt {3}-1\right )\right )}{3}}{a {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {2}{3}}}{12}+\frac {4 a^{2} \left (\frac {c_{1} {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}}{2}+\left (-i \sqrt {3}-1\right ) \left (a \,c_{1}^{2}+3 x \right ) a \right )}{3}}{a {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} c_{1}^{4} x +24576 a^{6} c_{1}^{2} x^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )}^{\frac {1}{3}}} \\ \end{align*}

Problem 9058

ODE	\[ \boxed {y^{\prime }+\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}=0} \]
program solution	\[ \frac {-y \ln \left (y\right )+\ln \left (y \ln \left (x \right )-2 y-1\right ) y-1}{y} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-2} x \right )+\ln \left (x \right )-2} \]

Problem 9059

ODE	\[ \boxed {y^{\prime }-\frac {-\ln \left (x \right )+2 y \ln \left (2 x \right ) x +\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}=0} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) \ln \left (x \right )^{2} x \left (\ln \left (2\right )+\ln \left (x \right )\right )-2 \ln \left (x \right ) \left (x^{2} \ln \left (2\right )^{2}+2 x^{2} \ln \left (x \right ) \ln \left (2\right )+\ln \left (x \right )^{2} x^{2}-\frac {\ln \left (2\right )}{2}\right ) \textit {\_Y}^{\prime }\left (x \right )+\left (x^{2} \ln \left (x \right )+\ln \left (2\right ) \left (x^{2}+1\right )\right ) \textit {\_Y} \left (x \right ) \left (\ln \left (2\right )+\ln \left (x \right )\right )^{2} x}{x \ln \left (x \right )^{2} \left (\ln \left (2\right )+\ln \left (x \right )\right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) \ln \left (x \right )}{\left (\ln \left (2\right )+\ln \left (x \right )\right ) \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) \ln \left (x \right )^{2} x \left (\ln \left (2\right )+\ln \left (x \right )\right )-2 \ln \left (x \right ) \left (x^{2} \ln \left (2\right )^{2}+2 x^{2} \ln \left (x \right ) \ln \left (2\right )+\ln \left (x \right )^{2} x^{2}-\frac {\ln \left (2\right )}{2}\right ) \textit {\_Y}^{\prime }\left (x \right )+\left (x^{2} \ln \left (x \right )+\ln \left (2\right ) \left (x^{2}+1\right )\right ) \textit {\_Y} \left (x \right ) \left (\ln \left (2\right )+\ln \left (x \right )\right )^{2} x}{x \ln \left (x \right )^{2} \left (\ln \left (2\right )+\ln \left (x \right )\right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x -\tan \left (c_{1} -x +\ln \left (2\right ) \operatorname {expIntegral}_{1}\left (-\ln \left (x \right )\right )\right ) \]

Problem 9060

ODE	\[ \boxed {y^{\prime }+\frac {y a b -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (y a -c +x b +a \sqrt {x}\right )}=0} \]
program solution	\[ \frac {\ln \left (x^{\frac {3}{2}} a b +a \left (y a -c \right ) \sqrt {x}+\left (y^{2}-2 x \right ) a^{2}+2 y \left (x b -c \right ) a +\left (x b -c \right )^{2}\right )}{2}-\frac {\operatorname {arctanh}\left (\frac {a \sqrt {x}+2 y a +2 x b -2 c}{3 a \sqrt {x}}\right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (x^{\frac {3}{2}} a b +b^{2} x^{2}-\sqrt {x}\, a c -2 a^{2} x -2 b c x +c^{2}-{\mathrm e}^{\operatorname {RootOf}\left (4 \,{\mathrm e}^{\textit {\_Z}}+9 \operatorname {sech}\left (-\frac {3 \textit {\_Z}}{2}+\frac {c_{1}}{2}\right )^{2} a^{2} x \right )}+\left (a \sqrt {x}+2 b x -2 c \right ) \textit {\_Z} +\textit {\_Z}^{2}\right )}{a} \]

Problem 9061

ODE	\[ \boxed {y^{\prime }-\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -2 x -2 \\ y \left (x \right ) &= \frac {\operatorname {LambertW}\left (\left (\ln \left (x +1\right )-c_{1} \right ) {\mathrm e}^{-2 x}\right )}{\ln \left (x +1\right )-c_{1}} \\ \end{align*}

Problem 9062

ODE	\[ \boxed {y^{\prime }-\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}=0} \]
program solution	\[ y = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{x^{2}+2 c_{1}}}{x}\right )}{2}+\frac {x^{2}}{2}+c_{1}} \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )^{2} x}{6 y \left (x \right )^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} \ln \left (\left ({\mathrm e}^{\textit {\_Z}}+9\right ) x \right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +9\right )}+9\right ) x}{54} \]

Problem 9063

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-y+x \right )}{x \left (x -y^{3}\right )}=0} \]
program solution	\[ -\ln \left (x \right )+\frac {x}{y}+\frac {y^{2}}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {2}{3}}+6 \ln \left (x \right )-6 c_{1}}{3 \left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {\left (\frac {i \sqrt {3}}{6}+\frac {1}{6}\right ) \left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {2}{3}}+\left (-\ln \left (x \right )+c_{1} \right ) \left (i \sqrt {3}-1\right )}{\left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {2}{3}}}{6}+\left (-\ln \left (x \right )+c_{1} \right ) \left (1+i \sqrt {3}\right )}{\left (-27 x +3 \sqrt {-24 \ln \left (x \right )^{3}+72 \ln \left (x \right )^{2} c_{1} -72 \ln \left (x \right ) c_{1}^{2}+24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 9064

ODE	\[ \boxed {y^{\prime }-\frac {\left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}=0} \]
program solution
Maple solution	\[ {\mathrm e}^{x}-\frac {2 \left (\int _{}^{y \left (x \right )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} \right )}{3}-c_{1} = 0 \]

Problem 9065

ODE	\[ \boxed {y^{\prime }-\frac {1+2 y}{x \left (-2+y^{2} x +2 x y^{3}\right )}=0} \]
program solution	\[ \frac {\left (-1-2 y\right ) x \ln \left (1+2 y\right )-8+\left (-4 y^{3}+2 y^{2}+2 y\right ) x}{\left (8 y+4\right ) x} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (x \,{\mathrm e}^{3 \textit {\_Z}}-4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+3 x \,{\mathrm e}^{\textit {\_Z}}+16\right )}}{2}-\frac {1}{2} \\ \end{align*}

Problem 9066

ODE	\[ \boxed {y^{\prime }-\frac {-x^{2}-x -a x -a +2 \sqrt {x^{2}+2 a x +a^{2}+4 y}\, x^{3}}{2 \left (x +1\right )}=0} \]
program solution
Maple solution	\[ c_{1} +\frac {2 x^{3}}{3}-x^{2}-2 \ln \left (x +1\right )+2 x -\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )} = 0 \]

Problem 9067

ODE	\[ \boxed {y^{\prime }-\frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9068

ODE	\[ \boxed {y^{\prime }-\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{x^{2}-3 x +4+{\mathrm e}^{-x} c_{1} +\operatorname {expIntegral}_{1}\left (-x -1\right ) {\mathrm e}^{-x -1}} \]

Problem 9069

ODE	\[ \boxed {y^{\prime }-\frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}=0} \]
program solution	\[ -2 \ln \left (x \right ) = \int _{}^{\frac {1-2 y \ln \left (x \right )}{y}}\frac {2 \textit {\_a} +2}{\textit {\_a}^{3}+2 \textit {\_a} +2}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {71 \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1} \right )-120}{\left (142 \ln \left (x \right )-71\right ) \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1} \right )-240 \ln \left (x \right )+48} \]

Problem 9070

ODE	\[ \boxed {y^{\prime }-\frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}=0} \]
program solution	\[ y = \frac {x^{4}+2 x^{3}+\left (c_{3} -1\right ) x^{2}-2 x +c_{3} -2}{x^{2}+c_{3} +2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1} \left (x^{4}+2 x^{3}-x^{2}-2 x -2\right )+x^{2}+1}{1+c_{1} \left (x^{2}+2 x \right )} \]

Problem 9071

ODE	\[ \boxed {y^{\prime }-\frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = x^{2}+\frac {\operatorname {LambertW}\left (-2 c_{1} {\mathrm e}^{\frac {4}{3} x^{3}-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]

Problem 9072

ODE	\[ \boxed {y^{\prime }-\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}=0} \]
program solution	\[ \frac {4 a x y^{3}-16 a^{2} y+x}{-8 a^{2} x y^{2}+32 a^{3}} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {192 c_{1}^{2} a^{3} x +x^{2}-x \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}+\left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {2}{3}}}{12 c_{1} x a \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (-i \sqrt {3}-1\right ) \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {2}{3}}}{24}+8 x \left (-\frac {\left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}}{96}+\left (i \sqrt {3}-1\right ) \left (a^{3} c_{1}^{2}+\frac {x}{192}\right )\right )}{c_{1} x a \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {2}{3}}}{24}+8 \left (-\frac {\left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}}{96}+\left (-i \sqrt {3}-1\right ) \left (a^{3} c_{1}^{2}+\frac {x}{192}\right )\right ) x}{c_{1} x a \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 a c_{1} x^{2} \sqrt {\frac {\left (324 a^{2} c_{1}^{4}+3 c_{1} \right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}+1536 c_{1}^{2} a^{4} x -49152 c_{1}^{4} a^{7}}{x}}-x^{3}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 9073

ODE	\[ \boxed {y^{\prime }-\frac {1+2 y}{x \left (-2+x y+2 y^{2} x \right )}=0} \]
program solution	\[ \frac {\left (1+2 y\right ) x \ln \left (1+2 y\right )-4-4 \left (y+c_{1} \right ) \left (y+\frac {1}{2}\right ) x}{\left (4 y+2\right ) x} = 0 \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+4\right )}}{2}-\frac {1}{2} \\ \end{align*}

Problem 9074

ODE	\[ \boxed {y^{\prime }-\frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {\left (x +c_{1} \right ) \left (2 c_{1} x^{2}+2 x^{3}-1\right )}}{2 c_{1} +2 x} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {\left (x +c_{1} \right ) \left (2 c_{1} x^{2}+2 x^{3}-1\right )}}{2 c_{1} +2 x} \\ \end{align*}

Problem 9075

ODE	\[ \boxed {y^{\prime }-\frac {\left (y^{2} a +b \,x^{2}\right )^{3} x}{a^{\frac {5}{2}} \left (y^{2} a +b \,x^{2}+a \right ) y}=0} \]
program solution
Maple solution	\[ \frac {\int _{\textit {\_b}}^{x}\frac {\left (b \,\textit {\_a}^{2}+a y \left (x \right )^{2}\right )^{3} \textit {\_a}}{b \left (y \left (x \right )^{2}+1\right ) a^{\frac {5}{2}}+a^{\frac {3}{2}} b^{2} \textit {\_a}^{2}+\left (b \,\textit {\_a}^{2}+a y \left (x \right )^{2}\right )^{3}}d \textit {\_a}}{a^{3}}-\frac {\int _{}^{y \left (x \right )}\frac {2 \left (\left (b \left (\textit {\_f}^{2}+1\right ) a^{\frac {5}{2}}+a^{\frac {3}{2}} b^{2} x^{2}+\left (a \,\textit {\_f}^{2}+b \,x^{2}\right )^{3}\right ) b \left (\int _{\textit {\_b}}^{x}\frac {\left (b \,\textit {\_a}^{2}+a \,\textit {\_f}^{2}\right )^{2} \textit {\_a} \left (2 b \,\textit {\_a}^{2}+2 a \,\textit {\_f}^{2}+3 a \right )}{{\left (b \left (\textit {\_f}^{2}+1\right ) a^{\frac {5}{2}}+a^{\frac {3}{2}} b^{2} \textit {\_a}^{2}+\left (b \,\textit {\_a}^{2}+a \,\textit {\_f}^{2}\right )^{3}\right )}^{2}}d \textit {\_a} \right )+\frac {b \,x^{2}}{2}+\frac {a \left (\textit {\_f}^{2}+1\right )}{2}\right ) \textit {\_f}}{b \left (\textit {\_f}^{2}+1\right ) a^{\frac {5}{2}}+a^{\frac {3}{2}} b^{2} x^{2}+\left (a \,\textit {\_f}^{2}+b \,x^{2}\right )^{3}}d \textit {\_f}}{\sqrt {a}}+c_{1} = 0 \]

Problem 9076

ODE	\[ \boxed {y^{\prime }+\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \arctan \left (\frac {\left (-\ln \left (x +1\right )+c_{1} \right ) \sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}+x}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}, \frac {\ln \left (x +1\right ) x -c_{1} x +\sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\left (\ln \left (x +1\right )-c_{1} \right ) \sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}+x}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}, \frac {\ln \left (x +1\right ) x -c_{1} x -\sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}\right ) \\ \end{align*}

Problem 9077

ODE	\[ \boxed {y^{\prime }+\frac {i \left (8 i x +16 y^{4}+8 y^{2} x^{2}+x^{4}\right )}{32 y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {\left (\left (1+i \sqrt {3}\right ) c_{1} \operatorname {AiryAi}\left (1, -\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, -\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )\right )}{2}\right ) \left (\operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )\right )}}{2 \operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +2 \operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {\left (\left (1+i \sqrt {3}\right ) c_{1} \operatorname {AiryAi}\left (1, -\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, -\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )\right )}{2}\right ) \left (\operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )\right )}}{2 \operatorname {AiryAi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right ) c_{1} +2 \operatorname {AiryBi}\left (-\frac {\left (-i+\sqrt {3}\right ) x}{2}\right )} \\ \end{align*}

Problem 9078

ODE	\[ \boxed {y^{\prime }-\frac {x}{-y+x^{4}+2 y^{2} x^{2}+y^{4}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {3 c_{1}^{4} x^{2}+24 c_{1}^{2} x^{4}+48 x^{6}+3 c_{1}^{3}+108 c_{1} x^{2}+81}\right )^{\frac {1}{3}}}{6}+\frac {c_{1}^{2}-12 x^{2}}{6 \left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {3 c_{1}^{4} x^{2}+24 c_{1}^{2} x^{4}+48 x^{6}+3 c_{1}^{3}+108 c_{1} x^{2}+81}\right )^{\frac {1}{3}}}-\frac {c_{1}}{6} \\ y \left (x \right ) &= -\frac {\left (\frac {i \sqrt {3}}{12}+\frac {1}{12}\right ) \left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {2}{3}}+\frac {c_{1} \left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}}{6}+\left (i \sqrt {3}-1\right ) \left (x^{2}-\frac {c_{1}^{2}}{12}\right )}{\left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {2}{3}}}{12}-\frac {c_{1} \left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}}{6}+\left (1+i \sqrt {3}\right ) \left (x^{2}-\frac {c_{1}^{2}}{12}\right )}{\left (-36 c_{1} x^{2}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 c_{1}^{2} x^{4}+\left (3 c_{1}^{4}+108 c_{1} \right ) x^{2}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 9079

ODE	\[ \boxed {y^{\prime }-\frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}=0} \]
program solution	\[ -\ln \left (x \right ) = \int _{}^{\frac {1-y \ln \left (x \right )}{y}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}+\textit {\_a} +1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {47 \operatorname {RootOf}\left (-27783 \left (\int _{}^{\textit {\_Z}}\frac {1}{2209 \textit {\_a}^{3}-9261 \textit {\_a} +9261}d \textit {\_a} \right )-7 \ln \left (x \right )+3 c_{1} \right )-84}{21+47 \left (-1+\ln \left (x \right )\right ) \operatorname {RootOf}\left (-27783 \left (\int _{}^{\textit {\_Z}}\frac {1}{2209 \textit {\_a}^{3}-9261 \textit {\_a} +9261}d \textit {\_a} \right )-7 \ln \left (x \right )+3 c_{1} \right )-84 \ln \left (x \right )} \]

Problem 9080

ODE	\[ \boxed {y^{\prime }+\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {\left (\operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right ) \left (\left (1+i \sqrt {3}\right ) c_{1} \operatorname {AiryAi}\left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )-2 x^{2} \left (\operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right )\right )}}{2 \operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +2 \operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {\left (\operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right ) \left (\left (1+i \sqrt {3}\right ) c_{1} \operatorname {AiryAi}\left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )-2 x^{2} \left (\operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right )\right )}}{2 \operatorname {AiryAi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1} +2 \operatorname {AiryBi}\left (-\left (-8 i\right )^{\frac {1}{3}} x \right )} \\ \end{align*}

Problem 9081

ODE	\[ \boxed {y^{\prime }+\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}=0} \]
program solution	\[ y = -\frac {{\mathrm e}^{-\left (\int \frac {\cot \left (x \right ) \left (\ln \left (2\right )+\ln \left (x \right )\right )^{2} x +\sec \left (x \right ) \csc \left (x \right ) x \ln \left (2\right )+\sec \left (x \right ) \csc \left (x \right ) x \ln \left (x \right )-1}{x \left (\ln \left (2\right )+\ln \left (x \right )\right )}d x \right )} \tan \left (x \right )}{\left (\ln \left (2\right )+\ln \left (x \right )\right ) x \left (c_{3} +\int {\mathrm e}^{-\left (\int \frac {\cot \left (x \right ) \left (\ln \left (2\right )+\ln \left (x \right )\right )^{2} x +\sec \left (x \right ) \csc \left (x \right ) x \ln \left (2\right )+\sec \left (x \right ) \csc \left (x \right ) x \ln \left (x \right )-1}{x \left (\ln \left (2\right )+\ln \left (x \right )\right )}d x \right )}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-\left (\int \frac {1+x \left (\ln \left (2\right )+\ln \left (x \right )\right ) \cot \left (x \right )}{x}d x \right )}}{-\left (\int \cot \left (x \right ) {\mathrm e}^{-\left (\int \frac {1+x \left (\ln \left (2\right )+\ln \left (x \right )\right ) \cot \left (x \right )}{x}d x \right )} \left (\ln \left (2\right )+\ln \left (x \right )\right ) x d x \right )+c_{1}} \]

Problem 9082

ODE	\[ \boxed {y^{\prime }-\frac {y \left (y+x \right )}{x \left (x +y^{3}\right )}=0} \]
program solution	\[ -\ln \left (x \right )-\frac {x}{y}+\frac {y^{2}}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+6 \ln \left (x \right )+6 c_{1}}{3 \left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (-i \sqrt {3}-1\right ) \left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}{6}+\left (i \sqrt {3}-1\right ) \left (\ln \left (x \right )+c_{1} \right )}{\left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}}{6}+\left (-i \sqrt {3}-1\right ) \left (\ln \left (x \right )+c_{1} \right )}{\left (27 x +3 \sqrt {-24 c_{1}^{3}-72 \ln \left (x \right ) c_{1}^{2}-72 \ln \left (x \right )^{2} c_{1} -24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 9083

ODE	\[ \boxed {y^{\prime }-\frac {\left (-y+x \right )^{2} \left (y+x \right )^{2} x}{y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\ y \left (x \right ) &= -\frac {\sqrt {\left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\ \end{align*}

Problem 9084

ODE	\[ \boxed {y^{\prime }-\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}=0} \]
program solution	\[ y = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{2 x +2 c_{1}}}{x}\right )}{2}+x +c_{1}} \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )^{2} x}{6 y \left (x \right )^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left (\left ({\mathrm e}^{\textit {\_Z}}+9\right ) x \right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +2 x \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54} \]

Problem 9085

ODE	\[ \boxed {y^{\prime }-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}=0} \]
program solution	\[ y = {\mathrm e}^{\frac {x^{3}}{2}+x \ln \left (x +1\right )+c_{1} x -x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (x +1\right )^{x} {\mathrm e}^{\frac {x \left (x^{2}+2 c_{1} -2 x \right )}{2}} \]

Problem 9086

ODE	\[ \boxed {y^{\prime }-\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \arctan \left (\frac {\left (2 x^{3}-3 x^{2}-6 \ln \left (x +1\right )+6 c_{1} +6 x \right ) \sqrt {36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}-36 c_{1} x^{2}+72 c_{1} x +36 c_{1}^{2}+36}+36 x}{36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}+\left (-36 c_{1} +36\right ) x^{2}+72 c_{1} x +36 c_{1}^{2}+36}, \frac {12 x^{4}-18 x^{3}-36 \ln \left (x +1\right ) x +36 c_{1} x +36 x^{2}-6 \sqrt {36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}-36 c_{1} x^{2}+72 c_{1} x +36 c_{1}^{2}+36}}{36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}+\left (-36 c_{1} +36\right ) x^{2}+72 c_{1} x +36 c_{1}^{2}+36}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )-6 c_{1} -6 x \right ) \sqrt {36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}-36 c_{1} x^{2}+72 c_{1} x +36 c_{1}^{2}+36}+36 x}{36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}+\left (-36 c_{1} +36\right ) x^{2}+72 c_{1} x +36 c_{1}^{2}+36}, \frac {12 x^{4}-18 x^{3}-36 \ln \left (x +1\right ) x +36 c_{1} x +36 x^{2}+6 \sqrt {36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}-36 c_{1} x^{2}+72 c_{1} x +36 c_{1}^{2}+36}}{36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 c_{1} -72 x \right ) \ln \left (x +1\right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1} -36\right ) x^{3}+\left (-36 c_{1} +36\right ) x^{2}+72 c_{1} x +36 c_{1}^{2}+36}\right ) \\ \end{align*}

Problem 9087

ODE	\[ \boxed {y^{\prime }-\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\frac {12 x}{3 x^{4}-4 x^{3}+6 x^{2}+12 \ln \left (x +1\right )-12 c_{1} -12 x}} \]

Problem 9088

ODE	\[ \boxed {y^{\prime }-\frac {x y+x^{3}+y^{2} x +y^{3}}{x^{2}}=0} \]
program solution	\[ 27 \left (\int _{}^{\frac {y-\frac {x}{3}}{x}}\frac {1}{27 \textit {\_a}^{3}-9 \textit {\_a} +29}d \textit {\_a} \right ) = x +c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )+x +c_{1} \right ) x \]

Problem 9089

ODE	\[ \boxed {y^{\prime }-\frac {y^{\frac {3}{2}}}{y^{\frac {3}{2}}+x^{2}-2 x y+y^{2}}=0} \]
program solution	\[ \ln \left (y-x \right )-\ln \left (2 y+\sqrt {y}-2 x \right )+\frac {\ln \left (y\right )}{2} = c_{1} \] Verified OK.
Maple solution	\[ \frac {4 \sqrt {y \left (x \right )}\, x^{2}-y \left (x \right )^{\frac {7}{2}} c_{1} +\left (2 c_{1} x +4\right ) y \left (x \right )^{\frac {5}{2}}+4 y \left (x \right )^{2}+\left (-c_{1} x^{2}-8 x +1\right ) y \left (x \right )^{\frac {3}{2}}-4 x y \left (x \right )}{\left (x -y \left (x \right )\right )^{2} y \left (x \right )^{\frac {3}{2}}} = 0 \]

Problem 9090

ODE	\[ \boxed {y^{\prime }-\frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {\left (-3+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )\right ) x^{2}}{9} \]

Problem 9091

ODE	\[ \boxed {y^{\prime }-\frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}=0} \]
program solution	\[ y = \frac {x^{2}}{4}+2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {c_{1}}{2}-\frac {x}{4}-\frac {1}{2}}}{8}\right )+\frac {x}{2}+1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2}}{4}+2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{4}-\frac {1}{2}}}{2}\right )+\frac {x}{2}+1 \]

Problem 9092

ODE	\[ \boxed {y^{\prime }-\frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {6 \operatorname {LambertW}\left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x \right ) {\mathrm e}^{-2 x}}{6}\right )}{-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x} \]

Problem 9093

ODE	\[ \boxed {y^{\prime }+\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-3 x^{3} \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) \left (\frac {\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} x^{3}}{3}+\frac {\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) x^{3}}{3}+\left (1+i\right ) \left (\operatorname {BesselJ}\left (-\frac {2}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (-\frac {2}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) \sqrt {6}\right )}}{3 \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) x} \\ y \left (x \right ) &= \frac {\sqrt {-3 x^{3} \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) \left (\frac {\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} x^{3}}{3}+\frac {\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) x^{3}}{3}+\left (1+i\right ) \left (\operatorname {BesselJ}\left (-\frac {2}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (-\frac {2}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) \sqrt {6}\right )}}{3 \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right ) c_{1} +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {2}{27}-\frac {2 i}{27}\right ) \sqrt {6}\, x^{3}\right )\right ) x} \\ \end{align*}

Problem 9094

ODE	\[ \boxed {y^{\prime }-\frac {\left (y^{2} x +1\right )^{3}}{x^{4} \left (y^{2} x +1+x \right ) y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {-\left (2+\left (1+i\right ) x \right ) x}}{2 x} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {-\left (2+\left (1+i\right ) x \right ) x}}{2 x} \\ y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {x \left (-2+\left (-1+i\right ) x \right )}}{2 x} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {x \left (-2+\left (-1+i\right ) x \right )}}{2 x} \\ -\frac {\ln \left (2 y \left (x \right )^{4} x^{2}+\left (2 x^{2}+4 x \right ) y \left (x \right )^{2}+x^{2}+2 x +2\right )}{10}+\frac {\arctan \left (2 y \left (x \right )^{4} x +\left (2 x +2\right ) y \left (x \right )^{2}+x +1\right )}{10}+\frac {\ln \left (x y \left (x \right )^{2}-x +1\right )}{5}+\frac {1}{2 x}-\frac {\arctan \left (2 y \left (x \right )^{2}+1\right )}{10}+c_{1} &= 0 \\ \end{align*}

Problem 9095

ODE	\[ \boxed {y^{\prime }-\frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}=0} \]
program solution	\[ y = -\frac {x^{2}}{4}+\operatorname {LambertW}\left (\frac {{\mathrm e}^{-2 c_{1} -x}}{4}\right )+x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{4}+\operatorname {LambertW}\left ({\mathrm e}^{-x} c_{1} \right )+x \]

Problem 9096

ODE	\[ \boxed {y^{\prime }+\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {x +c_{1}}{x}} \left (x +1\right )^{-\frac {1}{x}} \]

Problem 9097

ODE	\[ \boxed {y^{\prime }-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}=0} \]
program solution	\[ y = {\mathrm e}^{-x \ln \left (x +1\right )+x \ln \left (x \right )+c_{1} x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\frac {x c_{1}}{x +1}\right )^{x} \]

Problem 9098

ODE	\[ \boxed {y^{\prime }-\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x^{4}-4 x^{3}+6 x^{2}+12 c_{1} -12 x}{12 x}} \left (x +1\right )^{\frac {1}{x}} \]

Problem 9099

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x}=0} \]
program solution	\[ y = -\frac {\left (x +1\right )^{\ln \left (x \right )} \left (\frac {x^{2}-1}{x}\right )^{-\ln \left (x \right )} \left (1-x \right )^{\ln \left (x \right )} {\mathrm e}^{-\frac {\pi ^{2}}{6}+\frac {\operatorname {dilog}\left (-x^{2}+1\right )}{2}-\frac {\ln \left (x \right )^{2}}{2}}}{x \left (c_{3} +\int \frac {\left (x +1\right )^{\ln \left (x \right )} \left (\frac {x^{2}-1}{x}\right )^{-\ln \left (x \right )} \ln \left (\frac {x^{2}-1}{x}\right ) \left (1-x \right )^{\ln \left (x \right )} {\mathrm e}^{-\frac {\pi ^{2}}{6}+\frac {\operatorname {dilog}\left (-x^{2}+1\right )}{2}-\frac {\ln \left (x \right )^{2}}{2}}}{x}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {dilog}\left (x +1\right )}}{x \left (c_{1} {\mathrm e}^{\operatorname {dilog}\left (x \right )+\frac {\ln \left (x \right )^{2}}{2}} \left (\frac {x^{2}-1}{x}\right )^{\ln \left (x \right )} \left (x +1\right )^{-\ln \left (x \right )}+{\mathrm e}^{\operatorname {dilog}\left (x +1\right )}\right )} \]

Problem 9100

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-\ln \left (x \right )-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x +\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) y x^{2}\right )}{x \ln \left (x \right )}=0} \]
program solution	\[ y = -\frac {{\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}-1}{x}\right )^{2} x^{3}+\ln \left (\frac {x^{2}-1}{x}\right )^{2} x -\ln \left (\frac {x^{2}-1}{x}\right ) x^{2}+x^{2} \ln \left (x \right )+\ln \left (\frac {x^{2}-1}{x}\right )+\ln \left (x \right )}{\left (x^{3}-x \right ) \ln \left (x \right ) \ln \left (\frac {x^{2}-1}{x}\right )}d x} \ln \left (x \right )}{\ln \left (\frac {x^{2}-1}{x}\right ) x \left (c_{3} +\int {\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}-1}{x}\right )^{2} x^{3}+\ln \left (\frac {x^{2}-1}{x}\right )^{2} x -\ln \left (\frac {x^{2}-1}{x}\right ) x^{2}+x^{2} \ln \left (x \right )+\ln \left (\frac {x^{2}-1}{x}\right )+\ln \left (x \right )}{\left (x^{3}-x \right ) \ln \left (x \right ) \ln \left (\frac {x^{2}-1}{x}\right )}d x}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-\left (\int \frac {\ln \left (\frac {x^{2}-1}{x}\right ) x +\ln \left (x \right )}{\ln \left (x \right ) x}d x \right )}}{-\left (\int \frac {{\mathrm e}^{-\left (\int \frac {\ln \left (\frac {x^{2}-1}{x}\right ) x +\ln \left (x \right )}{\ln \left (x \right ) x}d x \right )} x \ln \left (\frac {x^{2}-1}{x}\right )}{\ln \left (x \right )}d x \right )+c_{1}} \]