2.17.92 Problems 9101 to 9200

Problem 9101

ODE	\[ \boxed {y^{\prime }-\frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}=0} \]
program solution	\[ y = -\frac {x^{2}}{8}+4 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {c_{1}}{4}-\frac {x}{16}-\frac {3}{4}}}{32}\right )+\frac {x}{4}+3 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{8}+4 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}-\frac {3}{4}}}{4}\right )+\frac {x}{4}+3 \]

Problem 9102

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

Problem 9103

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

Problem 9104

ODE	\[ \boxed {y^{\prime }-\frac {2 y^{6}}{y^{3}+2+16 y^{2} x +32 y^{4} x^{2}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (4096 c_{1}^{3} x^{3}+6 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+27 c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}\, c_{1} +96 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+27 c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}\, x +54 c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )^{\frac {1}{3}}+\frac {256 c_{1}^{2} x^{2}-12 c_{1} -192 x}{\left (4096 c_{1}^{3} x^{3}+6 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+27 c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}\, c_{1} +96 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+27 c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}\, x +54 c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )^{\frac {1}{3}}}+16 c_{1} x}{3 c_{1} +48 x} \\ y \left (x \right ) &= \frac {\frac {\left (-i \sqrt {3}-1\right ) {\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {2}{3}}}{6}+\frac {16 c_{1} x {\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {1}{3}}}{3}+\frac {128 \left (i \sqrt {3}-1\right ) \left (c_{1}^{2} x^{2}-\frac {3}{4} x -\frac {3}{64} c_{1} \right )}{3}}{{\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {1}{3}} \left (c_{1} +16 x \right )} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) {\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {2}{3}}}{6}+\frac {16 c_{1} x {\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {1}{3}}}{3}+\frac {128 \left (-i \sqrt {3}-1\right ) \left (c_{1}^{2} x^{2}-\frac {3}{4} x -\frac {3}{64} c_{1} \right )}{3}}{{\left (96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1} +256 x}+\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 x \,c_{1}^{2}+9216 c_{1} x^{2}\right )}^{\frac {1}{3}} \left (c_{1} +16 x \right )} \\ \end{align*}

Problem 9105

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

Problem 9106

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

Problem 9107

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

Problem 9108

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

Problem 9109

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

Problem 9110

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

Problem 9111

ODE	\[ \boxed {y^{\prime }-\frac {y \left (y+1\right )}{x \left (-y-1+y^{4} x \right )}=0} \]
program solution	\[ \frac {-x y^{3}-2 y \ln \left (y+1\right ) x +2 y^{2} x -2}{2 x y} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -1 \\ y \left (x \right ) &= {\mathrm e}^{\operatorname {RootOf}\left (x \,{\mathrm e}^{3 \textit {\_Z}}-5 x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+7 x \,{\mathrm e}^{\textit {\_Z}}-2 c_{1} x -2 x \textit {\_Z} -3 x +2\right )}-1 \\ \end{align*}

Problem 9112

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

Problem 9113

ODE	\[ \boxed {y^{\prime }-\frac {x^{3} y+x^{3}+y^{2} x +y^{3}}{\left (x -1\right ) x^{3}}=0} \]
program solution	\[ \frac {\ln \left (\frac {3 y+x}{x}\right )}{2}-\frac {\ln \left (\frac {9 \left (y-\frac {x}{3}\right )^{2}}{x^{2}}-\frac {6 \left (y-\frac {x}{3}\right )}{x}+10\right )}{4}-\frac {\arctan \left (-\frac {y-\frac {x}{3}}{x}+\frac {1}{3}\right )}{2}-\ln \left (x -1\right )+\ln \left (x \right )-c_{4} = 0 \] Verified OK.
Maple solution	\[ \frac {\ln \left (\frac {x +y \left (x \right )}{x}\right )}{2}-\frac {\ln \left (\frac {y \left (x \right )^{2}+x^{2}}{x^{2}}\right )}{4}+\frac {\arctan \left (\frac {y \left (x \right )}{x}\right )}{2}-\ln \left (x -1\right )+\ln \left (x \right )-c_{1} = 0 \]

Problem 9114

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

Problem 9115

ODE	\[ \boxed {y^{\prime }-\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}=0} \]
program solution	\[ y = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (6 x \,{\mathrm e}^{\frac {2}{3} x^{3}+x^{2}+2 c_{1}}\right )}{2}+\frac {x^{3}}{3}+\frac {x^{2}}{2}+c_{1}} x \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )^{2} x}{6 y \left (x \right )^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (2 x^{3} {\mathrm e}^{\textit {\_Z}}+3 x^{2} {\mathrm e}^{\textit {\_Z}}+3 \,{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-3 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+9}{x}\right )+9 c_{1} {\mathrm e}^{\textit {\_Z}}+3 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +27\right )}+9\right ) x}{54} \]

Problem 9116

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

Problem 9117

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

Problem 9118

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

Problem 9119

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

Problem 9120

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

Problem 9121

ODE	\[ \boxed {y^{\prime }-\frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {4 x^{2} {\mathrm e}^{\operatorname {RootOf}\left (8 x^{3} {\mathrm e}^{\textit {\_Z}}-24 x^{2} {\mathrm e}^{\textit {\_Z}}-36 x^{3}+6 \ln \left (\frac {2 \,{\mathrm e}^{\textit {\_Z}}-9}{\left (x +1\right )^{4}}\right ) {\mathrm e}^{\textit {\_Z}}+18 c_{1} {\mathrm e}^{\textit {\_Z}}-6 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +24 x \,{\mathrm e}^{\textit {\_Z}}+108 x^{2}-27 \ln \left (\frac {2 \,{\mathrm e}^{\textit {\_Z}}-9}{\left (x +1\right )^{4}}\right )-81 c_{1} +27 \textit {\_Z} -108 x +27\right )}-18 x^{2}-9}{4 \,{\mathrm e}^{\operatorname {RootOf}\left (8 x^{3} {\mathrm e}^{\textit {\_Z}}-24 x^{2} {\mathrm e}^{\textit {\_Z}}-36 x^{3}+6 \ln \left (\frac {2 \,{\mathrm e}^{\textit {\_Z}}-9}{\left (x +1\right )^{4}}\right ) {\mathrm e}^{\textit {\_Z}}+18 c_{1} {\mathrm e}^{\textit {\_Z}}-6 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +24 x \,{\mathrm e}^{\textit {\_Z}}+108 x^{2}-27 \ln \left (\frac {2 \,{\mathrm e}^{\textit {\_Z}}-9}{\left (x +1\right )^{4}}\right )-81 c_{1} +27 \textit {\_Z} -108 x +27\right )}-18} \]

Problem 9122

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

Problem 9123

ODE	\[ \boxed {y^{\prime }+\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 y \coth \left (x +1\right ) x -\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}=0} \]
program solution	\[ y = -x +\tan \left (\int \frac {\cosh \left (x \right ) \cosh \left (1\right )+\sinh \left (x \right ) \sinh \left (1\right )}{\ln \left (x -1\right ) \left (\sinh \left (x \right ) \cosh \left (1\right )+\cosh \left (x \right ) \sinh \left (1\right )\right )}d x +c_{1} \right ) \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 9124

ODE	\[ \boxed {y^{\prime }-\frac {2 x \ln \left (\frac {1}{x -1}\right )-\coth \left (\frac {x +1}{x -1}\right )+\coth \left (\frac {x +1}{x -1}\right ) y^{2}-2 \coth \left (\frac {x +1}{x -1}\right ) x^{2} y+\coth \left (\frac {x +1}{x -1}\right ) x^{4}}{\ln \left (\frac {1}{x -1}\right )}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9125

ODE	\[ \boxed {y^{\prime }-\frac {2 x^{2} \cosh \left (\frac {1}{x -1}\right )-2 x \cosh \left (\frac {1}{x -1}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +y^{2} x -2 x^{3} y+x^{5}}{\left (x -1\right ) \cosh \left (\frac {1}{x -1}\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{2} {\mathrm e}^{-4 \left (\int \frac {{\mathrm e}^{\frac {1}{x -1}} \left (x +1\right )}{\left (x -1\right ) \left ({\mathrm e}^{\frac {2}{x -1}}+1\right )}d x \right )+4 c_{1}}-x^{2}+{\mathrm e}^{-4 \left (\int \frac {{\mathrm e}^{\frac {1}{x -1}} \left (x +1\right )}{\left (x -1\right ) \left ({\mathrm e}^{\frac {2}{x -1}}+1\right )}d x \right )+4 c_{1}}+1\right ) {\mathrm e}^{4 \left (\int \frac {{\mathrm e}^{\frac {1}{x -1}} \left (x +1\right )}{\left (x -1\right ) \left ({\mathrm e}^{\frac {2}{x -1}}+1\right )}d x \right )}}{{\mathrm e}^{4 c_{1}}-{\mathrm e}^{4 \left (\int \frac {{\mathrm e}^{\frac {1}{x -1}} \left (x +1\right )}{\left (x -1\right ) \left ({\mathrm e}^{\frac {2}{x -1}}+1\right )}d x \right )}} \]

Problem 9126

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

Problem 9127

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

Problem 9128

ODE	\[ \boxed {y^{\prime }-\frac {y}{x \left (-1+y+y^{3} x^{2}+y^{4} x^{3}\right )}=0} \]
program solution	\[ \int _{}^{x}-\frac {1}{\textit {\_a} \left (\textit {\_a}^{3} y^{3}+\textit {\_a}^{2} y^{2}+1\right )}d \textit {\_a} +y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {-\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}-4-2 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}}{6 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {i \sqrt {3}\, \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4 i \sqrt {3}+\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+4}{12 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {-i \left (116+12 \sqrt {93}\right )^{\frac {2}{3}} \sqrt {3}+\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4 i \sqrt {3}-4 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}+4}{12 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ -y \left (x \right )+\int _{}^{x y \left (x \right )}\frac {1}{\textit {\_a} \left (\textit {\_a}^{3}+\textit {\_a}^{2}+1\right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

Problem 9129

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

Problem 9130

ODE	\[ \boxed {y^{\prime }-\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{3 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+{\mathrm e}^{\frac {3 x^{2}}{2}} y+3 y\right )}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (81+\left (9 \,{\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+7 \,{\mathrm e}^{3 x^{2}+\operatorname {RootOf}\left (\left (42 \sinh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right ) \sqrt {93}\, {\mathrm e}^{3 x^{2}+\textit {\_Z}} \cosh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )+406 \,{\mathrm e}^{3 x^{2}+\textit {\_Z}} \cosh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )^{2}-217 \,{\mathrm e}^{3 x^{2}+\textit {\_Z}}+93\right ) {\mathrm e}^{3 x^{2}}\right )}-3\right ) \textit {\_Z}^{2}+\left (54 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81\right ) \textit {\_Z} \right ) {\mathrm e}^{\frac {3 x^{2}}{2}} \]

Problem 9131

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) y x^{3}\right )}{x}=0} \]
program solution	\[ y = -\frac {\operatorname {sech}\left (\frac {x +1}{x -1}\right ) \left ({\mathrm e}^{\frac {2 x +2}{x -1}}+1\right ) {\mathrm e}^{-\frac {{\mathrm e}^{-\frac {2 x}{x -1}} \left (\left (x +5\right ) \left (x -1\right )^{2} {\mathrm e}^{\frac {3 x +1}{x -1}}+12 \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right ) \left (x -1\right ) {\mathrm e}^{\frac {-1+3 x}{x -1}}-4 \,\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) \left (x -1\right ) {\mathrm e}^{\frac {x +1}{x -1}}+8 x \,{\mathrm e}^{\frac {2 x}{x -1}}+{\mathrm e} \left (x +1\right ) \left (x -1\right )^{2}\right )}{4 x -4}}}{x \left (c_{3} +\int \left ({\mathrm e}^{\frac {2 x +2}{x -1}}+1\right ) \left (x +1\right ) {\mathrm e}^{-\frac {{\mathrm e}^{-\frac {2 x}{x -1}} \left (\left (x +5\right ) \left (x -1\right )^{2} {\mathrm e}^{\frac {3 x +1}{x -1}}+12 \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right ) \left (x -1\right ) {\mathrm e}^{\frac {-1+3 x}{x -1}}-4 \,\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) \left (x -1\right ) {\mathrm e}^{\frac {x +1}{x -1}}+8 x \,{\mathrm e}^{\frac {2 x}{x -1}}+{\mathrm e} \left (x +1\right ) \left (x -1\right )^{2}\right )}{4 x -4}}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-x -1}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}+\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) {\mathrm e}^{-1}-3 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (-c_{1} +\int {\mathrm e}^{\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-x -1}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}+\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) {\mathrm e}^{-1}-3 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )} \left (x +1\right ) \cosh \left (\frac {x +1}{x -1}\right )d x \right )} \]

Problem 9132

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

Problem 9133

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-1-{\mathrm e}^{\frac {x +1}{x -1}} x +y x^{2} {\mathrm e}^{\frac {x +1}{x -1}}-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x}=0} \]
program solution	\[ y = -\frac {{\mathrm e}^{\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}-6 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (2 c_{3} +\int \left (x +1\right ) {\mathrm e}^{\frac {-\left (x +5\right ) \left (x -1\right )^{2} {\mathrm e}^{\frac {x +1}{x -1}}-12 \left (x -1\right ) \operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right ) {\mathrm e}+2 x +2}{-2+2 x}}d x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}-6 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (c_{1} -\left (\int \left (x +1\right ) {\mathrm e}^{\frac {-\left (x +5\right ) \left (x -1\right )^{2} {\mathrm e}^{\frac {x +1}{x -1}}-12 \left (x -1\right ) {\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )+2 x +2}{2 x -2}}d x \right )\right )} \]

Problem 9134

ODE	\[ \boxed {y^{\prime }-\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 y^{2} b +8 y^{2} x +8 y^{3}}{\left (2 x -b \right )^{3}}=0} \]
program solution	\[ \ln \left (2 x -b \right ) = \int _{}^{\frac {y}{-2 x +b}}\frac {2}{8 \textit {\_a}^{3}-4 \textit {\_a}^{2}-2 \textit {\_a} -1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (-2 x +b \right )+c_{1} \right ) \left (-2 x +b \right )}{2} \]

Problem 9135

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

Problem 9136

ODE	\[ \boxed {y^{\prime }+\frac {-\frac {1}{x}-f_{1} \left (y+\frac {1}{x}\right )}{x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\operatorname {RootOf}\left (f_{1} \left (\textit {\_Z} \right )\right ) x -1}{x} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} \right ) x -1}{x} \\ \end{align*}

Problem 9137

ODE	\[ \boxed {y^{\prime }-\frac {f_{1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {2 \ln \left (x \right )+2 \operatorname {RootOf}\left (\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )-1}d \textit {\_a} \right )+c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {2 \ln \left (x \right )+2 \operatorname {RootOf}\left (\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )-1}d \textit {\_a} \right )+c_{1} \right )} \\ \end{align*}

Problem 9138

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

Problem 9139

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

Problem 9140

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

Problem 9141

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

Problem 9142

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

Problem 9143

ODE	\[ \boxed {y^{\prime }-\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 y^{2} x +64 y^{3}}{\left (4 x -5\right )^{3}}=0} \]
program solution	\[ 27 \left (\int _{}^{\frac {y-\frac {\left (\frac {64 x}{64 x^{3}-240 x^{2}+300 x -125}-\frac {80}{64 x^{3}-240 x^{2}+300 x -125}\right ) \left (64 x^{3}-240 x^{2}+300 x -125\right )}{192}}{x -\frac {5}{4}}}\frac {1}{27 \textit {\_a}^{3}-36 \textit {\_a} +38}d \textit {\_a} \right )-\ln \left (x -\frac {5}{4}\right )-c_{4} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (4 x -5\right )+c_{1} \right ) \left (4 x -5\right )}{4} \]

Problem 9144

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

Problem 9145

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

Problem 9146

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

Problem 9147

ODE	\[ \boxed {y^{\prime }-\frac {\left (-x^{3} \sqrt {a}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2}=0} \]
program solution
Maple solution	\[ \frac {\sqrt {x^{4} a +8 y \left (x \right )}}{4}+\frac {\left (-3 x^{4}-4 x^{3}-12 x \right ) \sqrt {a}}{12}-c_{1} = 0 \]

Problem 9148

ODE	\[ \boxed {y^{\prime }-\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {1}{\left (\sqrt {-2 x +c_{1}}-1\right ) x^{3}} \\ y \left (x \right ) &= -\frac {1}{\left (\sqrt {-2 x +c_{1}}+1\right ) x^{3}} \\ \end{align*}

Problem 9149

ODE	\[ \boxed {y^{\prime }-\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{81 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+{\mathrm e}^{\frac {3 x^{2}}{2}} y+3 y\right )}=0} \]
program solution
Maple solution	\[ 5 \ln \left (3\right )-5 \ln \left (7\right )+5 \ln \left (\frac {\left (-81 y \left (x \right )^{2}-243 y \left (x \right )\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+\left (3+y \left (x \right )\right )^{2} {\mathrm e}^{3 x^{2}}-243 y \left (x \right )^{2}}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )+3 y \left (x \right )\right )^{2}}\right )-\frac {30 \sqrt {93}\, \operatorname {arctanh}\left (\frac {\left (29 y \left (x \right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+87 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 y \left (x \right )\right ) \sqrt {93}}{\left (279 y \left (x \right )+837\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+837 y \left (x \right )}\right )}{31}-10 \ln \left (\frac {{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )}{{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )+3 y \left (x \right )}\right )+15 x^{2}-c_{1} = 0 \]

Problem 9150

ODE	\[ \boxed {y^{\prime }-\frac {\left (-y+x \right )^{3} \left (y+x \right )^{3} x}{\left (-y^{2}+x^{2}-1\right ) y}=0} \]
program solution
Maple solution	\[ -\left (\int _{\textit {\_b}}^{x}\frac {\left (-\textit {\_a} +y \left (x \right )\right )^{3} \left (\textit {\_a} +y \left (x \right )\right )^{3} \textit {\_a}}{-\textit {\_a}^{6}+3 \textit {\_a}^{4} y \left (x \right )^{2}-3 y \left (x \right )^{4} \textit {\_a}^{2}+y \left (x \right )^{6}+\textit {\_a}^{2}-y \left (x \right )^{2}-1}d \textit {\_a} \right )+\int _{}^{y \left (x \right )}\frac {2 \left (\left (-\textit {\_f}^{6}+3 \textit {\_f}^{4} x^{2}+\left (-3 x^{4}+1\right ) \textit {\_f}^{2}+x^{6}-x^{2}+1\right ) \left (\int _{\textit {\_b}}^{x}\frac {\left (\textit {\_a} -\textit {\_f} \right )^{2} \left (\textit {\_a} +\textit {\_f} \right )^{2} \textit {\_a} \left (2 \textit {\_a}^{2}-2 \textit {\_f}^{2}-3\right )}{\left (\textit {\_a}^{6}-3 \textit {\_a}^{4} \textit {\_f}^{2}+\left (3 \textit {\_f}^{4}-1\right ) \textit {\_a}^{2}-\textit {\_f}^{6}+\textit {\_f}^{2}+1\right )^{2}}d \textit {\_a} \right )+\frac {x^{2}}{2}-\frac {\textit {\_f}^{2}}{2}-\frac {1}{2}\right ) \textit {\_f}}{-\textit {\_f}^{6}+3 \textit {\_f}^{4} x^{2}+\left (-3 x^{4}+1\right ) \textit {\_f}^{2}+x^{6}-x^{2}+1}d \textit {\_f} +c_{1} = 0 \]

Problem 9151

ODE	\[ \boxed {y^{\prime }-\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \operatorname {arcsec}\left (\frac {3 x^{3} \ln \left (x \right )-x^{3}+9 c_{1}}{9 \ln \left (x \right )}\right ) \]

Problem 9152

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

Problem 9153

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

Problem 9154

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

Problem 9155

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

Problem 9156

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

Problem 9157

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

Problem 9158

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

Problem 9159

ODE	\[ \boxed {y^{\prime }-\frac {\left (\left (x^{2}+1\right )^{\frac {3}{2}} x^{2}+\left (x^{2}+1\right )^{\frac {3}{2}}+y^{2} \left (x^{2}+1\right )^{\frac {3}{2}}+y^{3} x^{2}+y^{3}\right ) x}{\left (x^{2}+1\right )^{3}}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {x^{2}+1}\, \left (19 \operatorname {RootOf}\left (-1296 \left (\int _{}^{\textit {\_Z}}\frac {1}{361 \textit {\_a}^{3}-432 \textit {\_a} +432}d \textit {\_a} \right )+2 \ln \left (x^{2}+1\right )+3 c_{1} \right )-6\right )}{18} \]

Problem 9160

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

Problem 9161

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

Problem 9162

ODE	\[ \boxed {y^{\prime }-\frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x y^{3}+2 y^{4} x \right )}=0} \]
program solution	\[ \frac {\left (1+2 y\right ) x \ln \left (1+2 y\right )+\left (-16 y-8\right ) x \ln \left (y+1\right )-8+\left (-4 y^{3}+10 y^{2}+6 y\right ) x}{\left (8 y+4\right ) x} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (16 \,{\mathrm e}^{\textit {\_Z}} x \ln \left ({\mathrm e}^{\textit {\_Z}}+1\right )-16 \,{\mathrm e}^{\textit {\_Z}} x \ln \left (2\right )+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{3 \textit {\_Z}}-8 x \,{\mathrm e}^{2 \textit {\_Z}}+7 x \,{\mathrm e}^{\textit {\_Z}}+16\right )}}{2}-\frac {1}{2} \\ \end{align*}

Problem 9163

ODE	\[ \boxed {y^{\prime }-\frac {1+2 \sqrt {1+4 x^{2} y}\, x^{3}+2 x^{5} \sqrt {1+4 x^{2} y}+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3}}=0} \]
program solution
Maple solution	\[ \frac {4 x^{6}+5 x^{5}+10 x^{3}+10 c_{1} x -10 \sqrt {4 x^{2} y \left (x \right )+1}}{10 x} = 0 \]

Problem 9164

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

Problem 9165

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

Problem 9166

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

Problem 9167

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

Problem 9168

ODE	\[ \boxed {y^{\prime }-\frac {\left (x^{4}+3 y^{2} x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (x +1\right )}=0} \]
program solution
Maple solution	\[ \frac {y \left (x \right )^{2} x}{6 y \left (x \right )^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {x \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{\left (x +1\right )^{2}}\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} -2 x \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54} \]

Problem 9169

ODE	\[ \boxed {y^{\prime }+\frac {1}{-\left (y^{3}\right )^{\frac {2}{3}} x -f_{1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{\frac {1}{3}} x}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9170

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

Problem 9171

ODE	\[ \boxed {y^{\prime }+\frac {1}{-\ln \left (x \right ) \left (y^{3}\right )^{\frac {2}{3}}-f_{1} \left (y^{3}+3 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x \right )\right )\right ) \ln \left (x \right ) \left (y^{3}\right )^{\frac {1}{3}}}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9172

ODE	\[ \boxed {y^{\prime }-\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{\frac {7}{2}}+100 x}{25 x}=0} \]
program solution	\[ y = \frac {2 \left (\ln \left (x \right )+c_{3} \right ) x^{\frac {7}{2}}+10 x c_{3} +10 x \ln \left (x \right )-5 \sqrt {x}}{5 \sqrt {x}\, \left (\ln \left (x \right )+c_{3} \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (10 c_{1} -10 \ln \left (x \right )\right ) \sqrt {x}+2 c_{1} x^{3}-2 x^{3} \ln \left (x \right )+5}{-5 \ln \left (x \right )+5 c_{1}} \]

Problem 9173

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

Problem 9174

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

Problem 9175

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

Problem 9176

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

Problem 9177

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

Problem 9178

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

Problem 9179

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

Problem 9180

ODE	\[ \boxed {y^{\prime }-\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +f_{1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-f_{1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (f_{1} \left (\frac {\left (\textit {\_Z} +1\right ) x}{\textit {\_Z}}\right ) x \textit {\_Z} +f_{1} \left (\frac {\left (\textit {\_Z} +1\right ) x}{\textit {\_Z}}\right ) x -\textit {\_Z} \right ) \\ y \left (x \right ) &= {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -\left (\int _{}^{\frac {x \,{\mathrm e}^{\textit {\_Z}}}{{\mathrm e}^{\textit {\_Z}}-1}}\frac {1}{\textit {\_a} \left (f_{1} \left (\textit {\_a} \right ) \textit {\_a} -1\right )}d \textit {\_a} \right )+c_{1} \right )}-1 \\ \end{align*}

Problem 9181

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

Problem 9182

ODE	\[ \boxed {y^{\prime }-f_{1} \left (y-\ln \left (\sinh \left (x \right )\right )\right )=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}} \]
program solution
Maple solution	\[ y \left (x \right ) = \ln \left (\sinh \left (x \right )\right )+\operatorname {RootOf}\left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9183

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

Problem 9184

ODE	\[ \boxed {y^{\prime }-f_{1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right )=\frac {1}{\sin \left (x \right )}} \]
program solution
Maple solution	\[ y \left (x \right ) = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} \right ) \]

Problem 9185

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

Problem 9186

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

Problem 9187

ODE	\[ \boxed {y^{\prime }-\frac {14 x y+12+2 x +y^{3} x^{3}+6 y^{2} x^{2}}{x^{2} \left (x y+2+x \right )}=0} \]
program solution	\[ -x +\frac {2 y+2}{y^{2} \left (x y+2\right )}-\frac {2}{\left (x y+2\right )^{2} y^{2}}-\frac {1}{y}-\frac {1}{2 y^{2}} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-2 \sqrt {-2 x +c_{1}}+x +2}{\left (\sqrt {-2 x +c_{1}}-1\right ) x} \\ y \left (x \right ) &= \frac {-2 \sqrt {-2 x +c_{1}}-x -2}{\left (\sqrt {-2 x +c_{1}}+1\right ) x} \\ \end{align*}

Problem 9188

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

Problem 9189

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

Problem 9190

ODE	\[ \boxed {y^{\prime }+\frac {\left (-\frac {1}{x}-f_{1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {2 \operatorname {RootOf}\left (x^{2}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+4 c_{1} \right )+2 x} \\ y \left (x \right ) &= -\sqrt {2 \operatorname {RootOf}\left (x^{2}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+4 c_{1} \right )+2 x} \\ \end{align*}

Problem 9191

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

Problem 9192

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

Problem 9193

ODE	\[ \boxed {y^{\prime }+\frac {-x -f_{1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {2 \operatorname {RootOf}\left (\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1} \right )+2 x} \\ y \left (x \right ) &= -\sqrt {2 \operatorname {RootOf}\left (\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1} \right )+2 x} \\ \end{align*}

Problem 9194

ODE	\[ \boxed {y^{\prime }-\frac {-\sin \left (2 y\right )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x}=0} \]
program solution	\[ -\frac {4 x \left (\left (x^{4}+\frac {5}{4} x^{3}+\frac {5}{2} x \right ) \cos \left (2 y\right )+x^{4}+\frac {5 x^{3}}{4}+\frac {5 x}{2}-5 \sin \left (2 y\right )\right )}{20 \cos \left (2 y\right )+20} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arctan \left (\frac {4 x^{5}+5 x^{4}+10 x^{2}+c_{1}}{20 x}\right ) \]

Problem 9195

ODE	\[ \boxed {y^{\prime }+\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-f_{1} \left ({\mathrm e}^{\frac {1}{x}} y\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (f_{1} \left (\textit {\_Z} \right )\right ) {\mathrm e}^{-\frac {1}{x}} \\ y \left (x \right ) &= \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} \right ) {\mathrm e}^{-\frac {1}{x}} \\ \end{align*}

Problem 9196

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

Problem 9197

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

Problem 9198

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

Problem 9199

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

Problem 9200

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