2.17.93 Problems 9201 to 9300

Problem 9201

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

Problem 9202

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

Problem 9203

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

Problem 9204

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

Problem 9205

ODE	\[ \boxed {y^{\prime }-\frac {-30 x^{3} y+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x}=0} \]
program solution	\[ 20 x^{\frac {7}{2}}+\left (-50 y-50\right ) \sqrt {x}-25 \ln \left (x \right )+2 x^{6}+\left (-10 y-10\right ) x^{3}+50 x +\frac {25 y^{2}}{2}+25 y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2 x^{3}}{5}-\sqrt {c_{1} +2 \ln \left (x \right )}+2 \sqrt {x}-1 \\ y \left (x \right ) &= \frac {2 x^{3}}{5}+2 \sqrt {x}+\sqrt {c_{1} +2 \ln \left (x \right )}-1 \\ \end{align*}

Problem 9206

ODE	\[ \boxed {y^{\prime }-\frac {1+2 y}{x \left (-2+x +y^{2} x +3 x y^{3}+2 x y+2 y^{4} x \right )}=0} \]
program solution	\[ \frac {\left (-54 y-27\right ) x \ln \left (1+2 y\right )-48+\left (-16 y^{4}-20 y^{3}+6 y^{2}+6 y\right ) x}{\left (48 y+24\right ) x} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (2 x \,{\mathrm e}^{4 \textit {\_Z}}-3 x \,{\mathrm e}^{3 \textit {\_Z}}-6 x \,{\mathrm e}^{2 \textit {\_Z}}+48 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+54 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+7 x \,{\mathrm e}^{\textit {\_Z}}+96\right )}}{2}-\frac {1}{2} \\ \end{align*}

Problem 9207

ODE	\[ \boxed {y^{\prime }-\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 y^{2} a \,x^{4}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512}=0} \]
program solution	\[ \int _{}^{y-\frac {\frac {3}{8} a \,x^{5}+x}{3 x}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\frac {x^{2}}{2}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{4} a}{8}-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (x^{2}-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+6 c_{1} \right )}{9} \]

Problem 9208

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

Problem 9209

ODE	\[ \boxed {y^{\prime }+\frac {y^{2} \left (x^{2} y-2 x -2 x y+y\right )}{2 \left (-2+x y-2 y\right ) x}=0} \]
program solution	\[ \frac {\left (x -2\right ) y-1}{y^{2}} = \frac {x^{2}}{4}-x +\frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {4}{\sqrt {c_{1} -8 \ln \left (x \right )}+2 x -4} \\ y \left (x \right ) &= -\frac {4}{\sqrt {c_{1} -8 \ln \left (x \right )}-2 x +4} \\ \end{align*}

Problem 9210

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

Problem 9211

ODE	\[ \boxed {y^{\prime }-\frac {1+y^{4}-8 y^{2} a x +16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y}=0} \]
program solution
Maple solution	\[ -\left (\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}}{\textit {\_a}^{6}-12 \textit {\_a}^{4} a x +48 \textit {\_a}^{2} a^{2} x^{2}-64 a^{3} x^{3}+\textit {\_a}^{4}-8 \textit {\_a}^{2} a x +16 a^{2} x^{2}-2 a +1}d \textit {\_a} \right )+x -c_{1} = 0 \]

Problem 9212

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

Problem 9213

ODE	\[ \boxed {y^{\prime }+\frac {2 a}{-y-2 a -2 y^{4} a +16 a^{2} x y^{2}-32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}}=0} \]
program solution	\[ \frac {y}{2 a} = \int _{}^{y^{2}-4 a x}-\frac {1}{8 a^{2} \left (\textit {\_a}^{3}+\textit {\_a}^{2}+1\right )}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )}{2 a}+\frac {\int _{}^{-4 a x +y \left (x \right )^{2}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a}}{8 a^{2}}-c_{1} = 0 \]

Problem 9214

ODE	\[ \boxed {y^{\prime }-\frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27}=0} \]
program solution	\[ \frac {-2 x^{2}-6 y-3}{\left (x^{2}+3 y\right )^{2}} = \frac {2 x}{3}+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-2 c_{1} x^{2}+2 x^{3}+3 \sqrt {2 c_{1} -2 x +1}+3}{-6 x +6 c_{1}} \\ y \left (x \right ) &= \frac {-2 c_{1} x^{2}+2 x^{3}-3 \sqrt {2 c_{1} -2 x +1}+3}{-6 x +6 c_{1}} \\ \end{align*}

Problem 9215

ODE	\[ \boxed {y^{\prime }+\frac {\left (-108 x^{\frac {3}{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{216}=0} \]
program solution	\[ \int _{}^{y-\frac {-\frac {x^{\frac {7}{2}}}{2}+\sqrt {x}}{3 \sqrt {x}}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\frac {2 x^{\frac {3}{2}}}{3}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{3}}{6}-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (2 x^{\frac {3}{2}}-243 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+9 c_{1} \right )}{9} \]

Problem 9216

ODE	\[ \boxed {y^{\prime }-\frac {\left (a^{3}+y^{4} a^{3}+2 a^{2} b \,x^{2} y^{2}+a \,b^{2} x^{4}+y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{\frac {7}{2}} y}=0} \]
program solution
Maple solution	\[ \frac {\int _{\textit {\_b}}^{x}\frac {\left (b^{3} \textit {\_a}^{6}+3 a \,b^{2} \textit {\_a}^{4} y \left (x \right )^{2}+3 a^{2} b \,\textit {\_a}^{2} y \left (x \right )^{4}+y \left (x \right )^{6} a^{3}+a \,b^{2} \textit {\_a}^{4}+2 a^{2} y \left (x \right )^{2} b \,\textit {\_a}^{2}+y \left (x \right )^{4} a^{3}+a^{3}\right ) \textit {\_a}}{y \left (x \right )^{6} a^{3}+3 a^{2} b \,\textit {\_a}^{2} y \left (x \right )^{4}+3 a \,b^{2} \textit {\_a}^{4} y \left (x \right )^{2}+b^{3} \textit {\_a}^{6}+y \left (x \right )^{4} a^{3}+2 a^{2} y \left (x \right )^{2} b \,\textit {\_a}^{2}+a \,b^{2} \textit {\_a}^{4}+a^{3}+a^{\frac {5}{2}} b}d \textit {\_a}}{a^{\frac {7}{2}}}-\left (\int _{}^{y \left (x \right )}\frac {2 \textit {\_f} \left (\frac {1}{2}+\left (a^{\frac {5}{2}} b +b^{3} x^{6}+3 a \,x^{4} \left (\textit {\_f}^{2}+\frac {1}{3}\right ) b^{2}+3 \left (\textit {\_f}^{2}+\frac {2}{3}\right ) a^{2} x^{2} \textit {\_f}^{2} b +\left (\textit {\_f}^{6}+\textit {\_f}^{4}+1\right ) a^{3}\right ) b \left (\int _{\textit {\_b}}^{x}\frac {\left (3 b \,\textit {\_a}^{2}+3 a \,\textit {\_f}^{2}+2 a \right ) \left (b \,\textit {\_a}^{2}+a \,\textit {\_f}^{2}\right ) \textit {\_a}}{\left (a^{\frac {5}{2}} b +\left (\textit {\_f}^{6}+\textit {\_f}^{4}+1\right ) a^{3}+3 \textit {\_a}^{2} \left (\textit {\_f}^{2}+\frac {2}{3}\right ) \textit {\_f}^{2} b \,a^{2}+3 \textit {\_a}^{4} b^{2} \left (\textit {\_f}^{2}+\frac {1}{3}\right ) a +b^{3} \textit {\_a}^{6}\right )^{2}}d \textit {\_a} \right )\right )}{a^{\frac {5}{2}} b +b^{3} x^{6}+3 a \,x^{4} \left (\textit {\_f}^{2}+\frac {1}{3}\right ) b^{2}+3 \left (\textit {\_f}^{2}+\frac {2}{3}\right ) a^{2} x^{2} \textit {\_f}^{2} b +\left (\textit {\_f}^{6}+\textit {\_f}^{4}+1\right ) a^{3}}d \textit {\_f} \right )+c_{1} = 0 \]

Problem 9217

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

Problem 9218

ODE	\[ \boxed {y^{\prime }+\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 y^{4} x^{2}+12 y^{2} x^{4}+x^{6}\right )}{128 y}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9219

ODE	\[ \boxed {y^{\prime }-\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 y^{2} x^{5}+3 y x^{4}-x^{3}}{x^{4}}=0} \]
program solution	\[ \frac {2}{x} = \int _{}^{\left (x y-1\right ) x}-\frac {2}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {9 x -3+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right ) x +3 c_{1} x -1\right )}{9 x^{2}} \]

Problem 9220

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

Problem 9221

ODE	\[ \boxed {y^{\prime }-\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )}=0} \]
program solution	\[ \frac {-2 x^{2} y+2 x -1}{x^{2} \left (x y-1\right )^{2}} = -\frac {2}{x}+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {\frac {c_{1} x +2}{x}}\, x -x +1}{\left (\sqrt {\frac {c_{1} x +2}{x}}-1\right ) x^{2}} \\ y \left (x \right ) &= \frac {\sqrt {\frac {c_{1} x +2}{x}}\, x +x -1}{\left (\sqrt {\frac {c_{1} x +2}{x}}+1\right ) x^{2}} \\ \end{align*}

Problem 9222

ODE	\[ \boxed {y^{\prime }+\frac {\left (-8-8 y^{3}+24 \,{\mathrm e}^{x} y^{\frac {3}{2}}-18 \,{\mathrm e}^{2 x}-8 y^{\frac {9}{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{\frac {3}{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}}=0} \]
program solution
Maple solution	\[ \frac {\left (-6 \,{\mathrm e}^{x}+4 y \left (x \right )^{\frac {3}{2}}\right ) \ln \left (2 y \left (x \right )^{\frac {3}{2}}-3 \,{\mathrm e}^{x}+2\right )+\left (6 \,{\mathrm e}^{x}-4 y \left (x \right )^{\frac {3}{2}}\right ) \ln \left (2 y \left (x \right )^{\frac {3}{2}}-3 \,{\mathrm e}^{x}\right )+\left (6 c_{1} -6 \,{\mathrm e}^{x}\right ) y \left (x \right )^{\frac {3}{2}}-9 c_{1} {\mathrm e}^{x}+9 \,{\mathrm e}^{2 x}-4}{-6 y \left (x \right )^{\frac {3}{2}}+9 \,{\mathrm e}^{x}} = 0 \]

Problem 9223

ODE	\[ \boxed {y^{\prime }-\frac {x}{-y+1+y^{4}+2 y^{2} x^{2}+x^{4}+y^{6}+3 y^{4} x^{2}+3 y^{2} x^{4}+x^{6}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {-6 x^{2} \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-2 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-4}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {-6 x^{2} \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-2 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-4}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (-12 x^{2}-4\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-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}}{12 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (-12 x^{2}-4\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-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}}{12 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (-12 x^{2}-4\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+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}}{12 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (-12 x^{2}-4\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+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}}{12 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ -y \left (x \right )+\frac {\left (\int _{}^{y \left (x \right )^{2}+x^{2}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )}{2}-c_{1} &= 0 \\ \end{align*}

Problem 9224

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

Problem 9225

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

Problem 9226

ODE	\[ \boxed {y^{\prime }-\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+y^{3} x^{3}+6 y^{2} x^{2}+12 x y+8}{x^{3}}=0} \]
program solution	\[ \int _{}^{y-\frac {1}{3}-\frac {2}{x}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right ) x -3 x -18}{9 x} \]

Problem 9227

ODE	\[ \boxed {y^{\prime }+\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 y^{2} x^{4}+3 y^{4} x^{2}+y^{6}\right )}{y}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9228

ODE	\[ \boxed {y^{\prime }-\frac {\left (-256 y a \,x^{2}-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 y^{2} a \,x^{4}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {8+\left (-\sqrt {-x^{2}+c_{1}}+1\right ) a \,x^{4}}{-8+8 \sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= \frac {-8+\left (-\sqrt {-x^{2}+c_{1}}-1\right ) a \,x^{4}}{8+8 \sqrt {-x^{2}+c_{1}}} \\ \end{align*}

Problem 9229

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

Problem 9230

ODE	\[ \boxed {y^{\prime }-\frac {\left (-108 y x^{\frac {3}{2}}+18 x^{\frac {9}{2}}-108 x^{\frac {3}{2}}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {9 c_{1} -12 x^{\frac {3}{2}}}\, x^{3}-3 x^{3}+18}{6 \sqrt {9 c_{1} -12 x^{\frac {3}{2}}}-18} \\ y \left (x \right ) &= \frac {\sqrt {9 c_{1} -12 x^{\frac {3}{2}}}\, x^{3}+3 x^{3}-18}{6 \sqrt {9 c_{1} -12 x^{\frac {3}{2}}}+18} \\ \end{align*}

Problem 9231

ODE	\[ \boxed {y^{\prime }-\frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {4 x^{2}-\sqrt {\frac {c_{1} x +2}{x}}+1}{4 \left (\sqrt {\frac {c_{1} x +2}{x}}-1\right ) x^{2}} \\ y \left (x \right ) &= \frac {-4 x^{2}-\sqrt {\frac {c_{1} x +2}{x}}-1}{4 \left (\sqrt {\frac {c_{1} x +2}{x}}+1\right ) x^{2}} \\ \end{align*}

Problem 9232

ODE	\[ \boxed {y^{\prime }-\frac {32 x^{5}+64 x^{6}+64 y^{2} x^{6}+32 y x^{4}+4 x^{2}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{64 x^{8}}=0} \]
program solution	\[ \int _{}^{y-\frac {\left (\frac {1}{x^{2}}+\frac {3}{4 x^{4}}\right ) x^{2}}{3}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} +\frac {1}{x}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {116 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right ) x +3 c_{1} x -1\right ) x^{2}-12 x^{2}-9}{36 x^{2}} \]

Problem 9233

ODE	\[ \boxed {y^{\prime }-\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}}=0} \]
program solution	\[ \frac {2 y a -\frac {1}{4 \left (y^{2}-4 a x \right )^{2}}-\frac {1}{2 \left (y^{2}-4 a x \right )}}{4 a^{2}} = c_{1} \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )}{2 a}-\frac {1}{16 \left (-4 a x +y \left (x \right )^{2}\right )^{2} a^{2}}+\frac {1}{32 x \,a^{3}-8 a^{2} y \left (x \right )^{2}}-c_{1} = 0 \]

Problem 9234

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

Problem 9235

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

Problem 9236

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

Problem 9237

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

Problem 9238

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

Problem 9239

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

Problem 9240

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

Problem 9241

ODE	\[ \boxed {y^{\prime }-\frac {4 x \left (a -1\right ) \left (a +1\right )}{4 y+y^{4} a^{2}-2 y^{2} a^{4} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 y^{2} x^{2}-x^{4}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (9^{\frac {2}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {2}{3}}+\left (-a^{2} c_{1} +c_{1} \right ) 9^{\frac {1}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}}+3 a^{6} x^{2}+\left (c_{1}^{2}-9 x^{2}\right ) a^{4}+\left (-2 c_{1}^{2}+9 x^{2}\right ) a^{2}-3 x^{2}+c_{1}^{2}\right ) 9^{\frac {2}{3}}}{9 {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}} \left (3 a^{2}-3\right )} \\ y \left (x \right ) &= \frac {\left (\left (-\frac {i \sqrt {3}}{3}-\frac {1}{3}\right ) 9^{\frac {2}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {2}{3}}+\left (-\frac {2 \,9^{\frac {1}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}} c_{1}}{3}+\left (i \sqrt {3}-1\right ) \left (a +1\right ) \left (a -1\right ) \left (a^{2} x^{2}-x^{2}+\frac {1}{3} c_{1}^{2}\right )\right ) \left (a +1\right ) \left (a -1\right )\right ) 9^{\frac {2}{3}}}{3 {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}} \left (6 a^{2}-6\right )} \\ y \left (x \right ) &= -\frac {9^{\frac {2}{3}} \left (\left (-\frac {i \sqrt {3}}{3}+\frac {1}{3}\right ) 9^{\frac {2}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {2}{3}}+\left (\frac {2 \,9^{\frac {1}{3}} {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}} c_{1}}{3}+\left (1+i \sqrt {3}\right ) \left (a +1\right ) \left (a -1\right ) \left (a^{2} x^{2}-x^{2}+\frac {1}{3} c_{1}^{2}\right )\right ) \left (a +1\right ) \left (a -1\right )\right )}{3 {\left (\left (3+\frac {\sqrt {-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}+6 c_{1}^{2} \left (a -1\right )^{4} \left (a +1\right )^{4} x^{4}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}+81}}{3}+\frac {\left (-a^{2}+1\right ) c_{1}^{3}}{9}+x^{2} \left (a -1\right )^{2} \left (a +1\right )^{2} c_{1} \right ) \left (a +1\right )^{2} \left (a -1\right )^{2}\right )}^{\frac {1}{3}} \left (6 a^{2}-6\right )} \\ \end{align*}

Problem 9242

ODE	\[ \boxed {y^{\prime }-\frac {x^{3}+y^{4} x^{3}+2 y^{2} x^{2}+x +y^{6} x^{3}+3 y^{4} x^{2}+3 y^{2} x +1}{x^{5} y}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {x \left (\frac {2^{\frac {2}{3}} \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {2}{3}}}{4}-\frac {2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}}{2}+x^{2}\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}}}{3 \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {x \left (\frac {2^{\frac {2}{3}} \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {2}{3}}}{4}-\frac {2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}}{2}+x^{2}\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}}}{3 \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= -\frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {4}\, \sqrt {\left (-\frac {2^{\frac {2}{3}} \left (1+i \sqrt {3}\right ) \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {2}{3}}}{4}-2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}}+x^{2} \left (i \sqrt {3}-1\right )\right ) x \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}}}}{12 \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {4}\, \sqrt {\left (-\frac {2^{\frac {2}{3}} \left (1+i \sqrt {3}\right ) \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {2}{3}}}{4}-2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}}+x^{2} \left (i \sqrt {3}-1\right )\right ) x \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}}}}{12 \left (x^{3} \left (-31+3 \sqrt {105}\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= -\frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {-4 x \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} \left (-\frac {2^{\frac {2}{3}} \left (i \sqrt {3}-1\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {2}{3}}}{4}+2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}+x^{2} \left (1+i \sqrt {3}\right )\right )}}{12 \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {-4 x \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} \left (-\frac {2^{\frac {2}{3}} \left (i \sqrt {3}-1\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {2}{3}}}{4}+2^{\frac {1}{3}} \left (x +3\right ) \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}}+x^{2} \left (1+i \sqrt {3}\right )\right )}}{12 \left (x^{3} \left (3 \sqrt {3}\, \sqrt {35}-31\right )\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {\sqrt {x \left (\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right ) x +c_{1} x +1\right ) x -1\right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right ) x +c_{1} x +1\right ) x -1\right )}}{x} \\ \end{align*}

Problem 9243

ODE	\[ \boxed {y^{\prime }-\frac {-2 x -y+1+y^{2} x^{2}+2 x^{3} y+x^{4}+y^{3} x^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x}=0} \]
program solution	\[ \int _{}^{x}\frac {-783-729 \textit {\_a}^{3} \left (y-\frac {3 x^{3}+x}{3 x^{2}}\right )^{3}+243 \left (\textit {\_a} +3\right ) \left (y-\frac {3 x^{3}+x}{3 x^{2}}\right )}{27 \textit {\_a}^{3} \left (y-\frac {3 x^{3}+x}{3 x^{2}}\right )^{3}-9 \textit {\_a} \left (y-\frac {3 x^{3}+x}{3 x^{2}}\right )+29}d \textit {\_a} = c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-9 x^{2}+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )-3}{9 x} \]

Problem 9244

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

Problem 9245

ODE	\[ \boxed {y^{\prime }-\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} a^{3} x -128 a^{4}}=0} \]
program solution	\[ -\frac {y}{2 a} = \int _{}^{\frac {y^{2} x -4 a}{x}}-\frac {1}{8 a^{2} \left (\textit {\_a}^{3}+\textit {\_a}^{2}+1\right )}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 9246

ODE	\[ \boxed {y^{\prime }+\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 y^{2} \ln \left (x \right )^{2}+y^{3} \ln \left (x \right )^{3}}{y x}=0} \]
program solution	\[ -\ln \left (x \right ) = \int _{}^{\frac {1-y \ln \left (x \right )}{y}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+2}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {9}{9 \ln \left (x \right )+56 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{3136 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \left (x \right )+3 c_{1} \right )-3} \]

Problem 9247

ODE	\[ \boxed {y^{\prime }-\frac {2 a \left (y^{2} x -4 a +x \right )}{-y^{3} x^{3}+4 y a \,x^{2}-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} a^{3} x -128 a^{4}}=0} \]
program solution	\[ \frac {-2 y a +\frac {x^{2} \left (-\frac {1}{2 \left (y^{2} x -4 a \right )^{2}}-\frac {1}{x \left (y^{2} x -4 a \right )}\right )}{2}}{4 a^{2}} = c_{1} \] Verified OK.
Maple solution	\[ \frac {y \left (x \right )^{4} x +\left (x -4 a \right ) y \left (x \right )^{2}-2 a}{2 y \left (x \right )^{4} \left (-x y \left (x \right )^{2}+4 a \right )^{2} a}+\frac {8 a y \left (x \right )^{5}+1+2 y \left (x \right )^{2}}{16 y \left (x \right )^{4} a^{2}}+c_{1} = 0 \]

Problem 9248

ODE	\[ \boxed {y^{\prime }+\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 y^{2} \ln \left (x \right )^{2}+8 y^{3} \ln \left (x \right )^{3}}{y x}=0} \]
program solution	\[ -2 \ln \left (x \right ) = \int _{}^{\frac {1-2 y \ln \left (x \right )}{y}}\frac {2}{\textit {\_a}^{3}+\textit {\_a}^{2}+3}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {9}{18 \ln \left (x \right )+83 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{6889 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \left (x \right )+3 c_{1} \right )-3} \]

Problem 9249

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

Problem 9250

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

Problem 9251

ODE	\[ \boxed {y^{\prime }-\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 y^{2} x +96 y^{4} x^{2}+128 y^{6} x^{3}}=0} \]
program solution
Maple solution	\[ x -\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{64 \textit {\_a}^{3}+16 \textit {\_a}^{2}+1}d \textit {\_a} \right ) y \left (x \right )+c_{1} y \left (x \right )+1\right )+\frac {1}{4 y \left (x \right )^{2}} = 0 \]

Problem 9252

ODE	\[ \boxed {y^{\prime }-\frac {y^{\frac {3}{2}} \left (x -y+\sqrt {y}\right )}{y^{\frac {3}{2}} x -y^{\frac {5}{2}}+y^{2}+x^{3}-3 x^{2} y+3 y^{2} x -y^{3}}=0} \]
program solution	\[ \ln \left (y-x \right )-\frac {\ln \left (2 y-\sqrt {y}-2 x \right )}{3}+\frac {\ln \left (y\right )}{2}-\frac {2 \ln \left (y+\sqrt {y}-x \right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ -\frac {\left (c_{1} x^{6}+80 x^{3}-54 x^{2}-12 x -1\right ) y \left (x \right )^{\frac {7}{2}}+\left (-6 c_{1} x^{5}-60 x^{2}+36 x +6\right ) y \left (x \right )^{\frac {9}{2}}+\left (15 c_{1} x^{4}+24 x -9\right ) y \left (x \right )^{\frac {11}{2}}+\left (-60 x^{4}+36 x^{3}+6 x^{2}\right ) y \left (x \right )^{\frac {5}{2}}+\left (-20 c_{1} x^{3}-4\right ) y \left (x \right )^{\frac {13}{2}}+\left (24 x^{5}-9 x^{4}\right ) y \left (x \right )^{\frac {3}{2}}+15 y \left (x \right )^{\frac {15}{2}} c_{1} x^{2}-6 y \left (x \right )^{\frac {17}{2}} c_{1} x +y \left (x \right )^{\frac {19}{2}} c_{1} -4 x^{6} \sqrt {y \left (x \right )}+12 \left (x -y \left (x \right )\right )^{3} \left (y \left (x \right )^{2}+\left (-2 x -\frac {1}{3}\right ) y \left (x \right )+x^{2}\right ) y \left (x \right )}{y \left (x \right )^{\frac {7}{2}} \left (x -y \left (x \right )\right )^{6}} = 0 \]

Problem 9253

ODE	\[ \boxed {y^{\prime }-\frac {2 y^{6} \left (1+4 y^{2} x +y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 y^{2} x +96 y^{4} x^{2}+128 y^{6} x^{3}}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9254

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

Problem 9255

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

Problem 9256

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

Problem 9257

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

Problem 9258

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

Problem 9259

ODE	\[ \boxed {y^{\prime }-\frac {-8 y^{3} x^{2}+16 y^{2} x +16 x y^{3}-8+12 x y-6 y^{2} x^{2}+y^{3} x^{3}}{16 \left (-2+x y-2 y\right ) x}=0} \]
program solution	\[ \frac {-16-8 x^{2} y+\left (16 y+16\right ) x}{x^{2} \left (-2+x y\right )^{2}} = \frac {\ln \left (x \right )}{2}+\frac {4}{x}-\frac {4}{x^{2}}+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2 \sqrt {c_{1} +8 \ln \left (x \right )}+8}{x \sqrt {c_{1} +8 \ln \left (x \right )}+4 x -8} \\ y \left (x \right ) &= \frac {2 \sqrt {c_{1} +8 \ln \left (x \right )}-8}{x \sqrt {c_{1} +8 \ln \left (x \right )}-4 x +8} \\ \end{align*}

Problem 9260

ODE	\[ \boxed {y^{\prime }+\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8}=0} \]
program solution	\[ \int _{}^{y-\frac {-\frac {3 \,{\mathrm e}^{-x^{2}} x^{3}}{2}+x}{3 x}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\frac {x^{2}}{2}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-x^{2}} x^{2}}{2}-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (x^{2}-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+6 c_{1} \right )}{9} \]

Problem 9261

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

Problem 9262

ODE	\[ \boxed {y^{\prime }+\frac {16 x y^{3}-8 y^{3}-8 y+8 y^{2} x -2 y^{3} x^{2}-8+12 x y-6 y^{2} x^{2}+y^{3} x^{3}}{32 y x}=0} \]
program solution	\[ -\frac {\ln \left (x \right )}{2} = \int _{}^{\frac {2-x y}{2 y}}\frac {2}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {18}{58 \operatorname {RootOf}\left (-324 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \left (x \right )+12 c_{1} \right )+9 x -6} \]

Problem 9263

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

Problem 9264

ODE	\[ \boxed {y^{\prime }-\frac {-3 x^{2} y-2 x^{3}-2 x -y^{2} x -y+y^{3} x^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x \left (x y+x^{2}+1\right )}=0} \]
program solution	\[ -\frac {\ln \left (1+2 x^{5}+\left (4 y+1\right ) x^{4}+\left (2 y^{2}+2 y\right ) x^{3}+\left (y^{2}+2\right ) x^{2}+2 x y\right )}{2}+\ln \left (y+x \right ) = -\ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-\sqrt {-2 x +c_{1}}\, x^{2}+x^{2}+1}{\left (\sqrt {-2 x +c_{1}}-1\right ) x} \\ y \left (x \right ) &= \frac {-\sqrt {-2 x +c_{1}}\, x^{2}-x^{2}-1}{\left (\sqrt {-2 x +c_{1}}+1\right ) x} \\ \end{align*}

Problem 9265

ODE	\[ \boxed {y^{\prime }-\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 y^{2} {\mathrm e}^{3 x^{2}}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {369 \,{\mathrm e}^{\frac {3 x^{2}}{2}}}{123+123 \,{\mathrm e}^{\frac {3 x^{2}}{2}}-136 \operatorname {RootOf}\left (-41 x^{2}-50243409 \left (\int _{}^{\textit {\_Z}}\frac {1}{9248 \textit {\_a}^{3}-1860867 \textit {\_a} +1860867}d \textit {\_a} \right )+27 c_{1} \right )} \]

Problem 9266

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

Problem 9267

ODE	\[ \boxed {y^{\prime }-y^{2}-\frac {x^{2} y}{4}+x y-y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 y^{2} x}{2}-\frac {3 y x^{4}}{16}-\frac {3 x^{3} y}{4}=\frac {1}{2} x +1-\frac {1}{8} x^{4}+\frac {1}{8} x^{3}+\frac {1}{4} x^{2}-\frac {1}{64} x^{6}-\frac {3}{32} x^{5}} \]
program solution	\[ \int _{}^{y-\frac {1}{3}+\frac {x^{2}}{4}+\frac {x}{2}}\frac {1}{\frac {31}{54}+\textit {\_a}^{3}-\frac {1}{3} \textit {\_a}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2}}{4}+\frac {x}{2}+\operatorname {RootOf}\left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9268

ODE	\[ \boxed {y^{\prime }-y^{2}-\frac {7 x^{2} y}{2}+2 x y-y^{3}-\frac {3 y^{2} x^{2}}{4}+3 y^{2} x -\frac {3 y x^{4}}{16}+\frac {3 x^{3} y}{2}=-\frac {1}{2} x +1+\frac {13}{16} x^{4}-\frac {3}{2} x^{3}+x^{2}+\frac {1}{64} x^{6}-\frac {3}{16} x^{5}} \]
program solution	\[ \int _{}^{y-\frac {1}{3}-\frac {x^{2}}{4}+x}\frac {1}{\frac {2}{27}+\textit {\_a}^{3}-\frac {1}{3} \textit {\_a}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}-4\right ) {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +x \,{\mathrm e}^{\textit {\_Z}}-4 \ln \left ({\mathrm e}^{\textit {\_Z}}-4\right )-4 c_{1} +4 \textit {\_Z} -4 x +4\right )}}{4}-1-\frac {x^{2}}{4}+x \]

Problem 9269

ODE	\[ \boxed {y^{\prime }-y^{2}-\frac {7 x^{2} y}{16}+\frac {x y}{2}-y^{3}-\frac {3 y^{2} x^{2}}{8}+\frac {3 y^{2} x}{4}-\frac {3 y x^{4}}{64}+\frac {3 x^{3} y}{16}=-\frac {1}{4} x +1+\frac {5}{128} x^{4}-\frac {5}{64} x^{3}+\frac {1}{16} x^{2}+\frac {1}{512} x^{6}-\frac {3}{256} x^{5}} \]
program solution	\[ \int _{}^{y-\frac {1}{3}-\frac {x^{2}}{8}+\frac {x}{4}}\frac {1}{\frac {89}{108}+\textit {\_a}^{3}-\frac {1}{3} \textit {\_a}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{8}+\frac {x}{4}+\operatorname {RootOf}\left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {1}{4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+3}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9270

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

Problem 9271

ODE	\[ \boxed {y^{\prime }-\frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 x y+4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 y^{2} x +3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x}=0} \]
program solution	\[ \int _{}^{y-\frac {\left (3 x -3+\frac {1}{x}\right ) x}{3}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\ln \left (x \right )-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x^{2}+x -\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1} \right )}{9} \]

Problem 9272

ODE	\[ \boxed {y^{\prime }-\frac {-32 x y+16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 y^{2} x -12 y x^{4}-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64}=0} \]
program solution	\[ x = -\frac {2 \ln \left (2 \left (-\frac {x^{2}}{4}-\frac {x}{2}+y\right )^{2}-\frac {x^{2}}{2}-x +2 y+1\right )}{5}+\frac {2 \arctan \left (\frac {x^{2}}{2}-2 y+x -1\right )}{5}+\frac {4 \ln \left (-\frac {x^{2}}{4}-\frac {x}{2}+y-1\right )}{5}+c_{1} \] Verified OK.
Maple solution	\[ x +\frac {2 \ln \left (2\right )}{5}+\frac {2 \ln \left (16 y \left (x \right )^{2}+\left (-8 x^{2}-16 x +16\right ) y \left (x \right )+x^{4}+4 x^{3}-8 x +8\right )}{5}-\frac {2 \arctan \left (-2 y \left (x \right )+\frac {x^{2}}{2}+x -1\right )}{5}-\frac {4 \ln \left (4 y \left (x \right )-x^{2}-2 x -4\right )}{5}-c_{1} = 0 \]

Problem 9273

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

Problem 9274

ODE	\[ \boxed {y^{\prime }-\frac {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 y^{2} x +12 y x^{4}-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64}=0} \]
program solution	\[ x = \int _{}^{y}\frac {\frac {1}{4} x^{2}-x +\textit {\_a} +1}{\left (\frac {1}{4} x^{2}-x +\textit {\_a} \right )^{3}-\frac {x^{2}}{4}+x -\textit {\_a} -1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{4}+x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} +c_{1} \right ) \]

Problem 9275

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

Problem 9276

ODE	\[ \boxed {y^{\prime }-\frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 y^{2} x +24 y x^{4}-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512}=0} \]
program solution	\[ x = \int _{}^{y}\frac {\frac {1}{2} x^{2}-x +4 \textit {\_a} +4}{4 \left (\frac {1}{8} x^{2}-\frac {1}{4} x +\textit {\_a} \right )^{3}-\frac {x^{2}}{8}+\frac {x}{4}-\textit {\_a} -1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{8}+\frac {x}{4}+\operatorname {RootOf}\left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{4 \textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9277

ODE	\[ \boxed {y^{\prime }-\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 y^{2} a \,x^{2}+96 y^{2} b x +12 y a^{2} x^{4}+48 y a \,x^{3} b +48 y b^{2} x^{2}+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,b^{2} x^{4}+8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 x b +64}=0} \]
program solution	\[ -\frac {x b}{2} = \int _{}^{y}-\frac {b \left (\textit {\_a} +\frac {1}{4} a \,x^{2}+\frac {1}{2} x b +1\right )}{2 \left (\textit {\_a} +\frac {1}{4} a \,x^{2}+\frac {1}{2} x b \right )^{3}+\left (\textit {\_a} +\frac {1}{4} a \,x^{2}+\frac {1}{2} x b \right ) b +b}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {a \,x^{2}}{4}-\frac {b x}{2}+\operatorname {RootOf}\left (b x -2 b \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{2 \textit {\_a}^{3}+\textit {\_a} b +b}d \textit {\_a} \right )+2 c_{1} \right ) \]

Problem 9278

ODE	\[ \boxed {y^{\prime }-\frac {-32 x y-8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 y^{2} a x +12 y x^{4}+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 a \,x^{5}+12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64}=0} \]
program solution	\[ -\frac {x}{2} = \int _{}^{y}-\frac {\frac {1}{4} x^{2}+\frac {1}{2} a x +\textit {\_a} +1}{2 \left (\frac {1}{4} x^{2}+\frac {1}{2} a x +\textit {\_a} \right )^{3}+\left (\frac {1}{4} x^{2}+\frac {1}{2} a x +\textit {\_a} \right ) a +a}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{4}-\frac {a x}{2}+\operatorname {RootOf}\left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{2 \textit {\_a}^{3}+\textit {\_a} a +a}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9279

ODE	\[ \boxed {y^{\prime }-\frac {\left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-4 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+4 x^{2} {\mathrm e}^{-2 x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 \,{\mathrm e}^{-x^{2}} y-8 \,{\mathrm e}^{-x^{2}}\right ) x}{-8 y+4 x^{2} {\mathrm e}^{-x^{2}}-8}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2+x^{2} \left (\sqrt {-x^{2}+c_{1}}-1\right ) {\mathrm e}^{-x^{2}}}{2 \sqrt {-x^{2}+c_{1}}-2} \\ y \left (x \right ) &= \frac {-2+x^{2} \left (\sqrt {-x^{2}+c_{1}}+1\right ) {\mathrm e}^{-x^{2}}}{2 \sqrt {-x^{2}+c_{1}}+2} \\ \end{align*}

Problem 9280

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

Problem 9281

ODE	\[ \boxed {y^{\prime }+\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 x y+60 y^{5}-36 x y^{3}-72 y^{2} x -24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (12 c_{1} {\mathrm e}^{4 \textit {\_Z}}+2 \,{\mathrm e}^{4 \textit {\_Z}} \textit {\_Z} +18 c_{1} {\mathrm e}^{3 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z} +36 \,{\mathrm e}^{2 \textit {\_Z}} c_{1} +6 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+36 c_{1} {\mathrm e}^{\textit {\_Z}}+6 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} -36 c_{1} x -6 x \textit {\_Z} +36\right )} \]

Problem 9282

ODE	\[ \boxed {y^{\prime }-\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+x y+x +y^{3}+3 y^{2} x^{2}-3 y^{2} x +3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )}=0} \]
program solution	\[ \frac {-2 x^{2}+2 x -2 y-1}{\left (y+x^{2}-x \right )^{2}} = 2 \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (-x^{2}+x \right ) \sqrt {c_{1} -2 \ln \left (x \right )}+x^{2}-x +1}{-1+\sqrt {c_{1} -2 \ln \left (x \right )}} \\ y \left (x \right ) &= \frac {\left (-x^{2}+x \right ) \sqrt {c_{1} -2 \ln \left (x \right )}-x^{2}+x -1}{1+\sqrt {c_{1} -2 \ln \left (x \right )}} \\ \end{align*}

Problem 9283

ODE	\[ \boxed {y^{\prime }-y^{2}-\frac {y a \,x^{2}}{2}-y x b -y^{3}-\frac {3 y^{2} a \,x^{2}}{4}-\frac {3 y^{2} b x}{2}-\frac {3 y a^{2} x^{4}}{16}-\frac {3 y a \,x^{3} b}{4}-\frac {3 y b^{2} x^{2}}{4}=-\frac {1}{2} a x +1+\frac {1}{16} a^{2} x^{4}+\frac {1}{4} a b \,x^{3}+\frac {1}{4} b^{2} x^{2}+\frac {1}{64} a^{3} x^{6}+\frac {3}{32} a^{2} x^{5} b +\frac {3}{16} a \,b^{2} x^{4}+\frac {1}{8} b^{3} x^{3}} \]
program solution	\[ \int _{}^{y-\frac {1}{3}-\frac {a \,x^{2}}{4}-\frac {x b}{2}}\frac {1}{\frac {1}{2} b +\frac {29}{27}+\textit {\_a}^{3}-\frac {1}{3} \textit {\_a}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {a \,x^{2}}{4}-\frac {b x}{2}+\operatorname {RootOf}\left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+b +2}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9284

ODE	\[ \boxed {y^{\prime }-y^{2}-\frac {x^{2} y}{2}-a x y-y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 y^{2} a x}{2}-\frac {3 y x^{4}}{16}-\frac {3 y a \,x^{3}}{4}-\frac {3 y a^{2} x^{2}}{4}=-\frac {1}{2} x +1+\frac {1}{16} x^{4}+\frac {1}{4} a \,x^{3}+\frac {1}{4} a^{2} x^{2}+\frac {1}{64} x^{6}+\frac {3}{32} a \,x^{5}+\frac {3}{16} a^{2} x^{4}+\frac {1}{8} a^{3} x^{3}} \]
program solution	\[ \int _{}^{y-\frac {1}{3}-\frac {x^{2}}{4}-\frac {a x}{2}}\frac {1}{\frac {1}{2} a +\frac {29}{27}+\textit {\_a}^{3}-\frac {1}{3} \textit {\_a}}d \textit {\_a} = x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{4}-\frac {a x}{2}+\operatorname {RootOf}\left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+a +2}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 9285

ODE	\[ \boxed {y^{\prime }+\frac {-y+\sqrt {y^{2}+x^{2}}\, x^{2}-x y \sqrt {y^{2}+x^{2}}+x^{4} \sqrt {y^{2}+x^{2}}-x^{3} \sqrt {y^{2}+x^{2}}\, y+x^{5} \sqrt {y^{2}+x^{2}}-x^{4} \sqrt {y^{2}+x^{2}}\, y}{x}=0} \]
program solution
Maple solution	\[ \ln \left (\frac {x \left (\sqrt {2 y \left (x \right )^{2}+2 x^{2}}+y \left (x \right )+x \right )}{y \left (x \right )-x}\right )+\frac {\left (4 x^{5}+5 x^{4}+10 x^{2}\right ) \sqrt {2}}{20}-c_{1} +\ln \left (2\right )-\ln \left (x \right ) = 0 \]

Problem 9286

ODE	\[ \boxed {y^{\prime }-\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+\ln \left (x \right )^{2} x^{3}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+\ln \left (x \right )^{2} x^{4}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {20 x}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}}}{x} \]

Problem 9287

ODE	\[ \boxed {y^{\prime }-\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{\frac {7}{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 y x^{6}+600 x^{\frac {7}{2}} y+1500 x y-8 x^{9}-120 x^{\frac {13}{2}}-600 x^{4}-1000 x^{\frac {3}{2}}}{125 x}=0} \]
program solution	\[ \int _{}^{y-\frac {\left (-\frac {6 x^{2}}{5}-\frac {6}{\sqrt {x}}+\frac {1}{x}\right ) x}{3}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\ln \left (x \right )-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {18 x^{\frac {7}{2}}+145 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1} \right ) \sqrt {x}-15 \sqrt {x}+90 x}{45 \sqrt {x}} \]

Problem 9288

ODE	\[ \boxed {y^{\prime }-\frac {-150 x^{3} y+60 x^{6}+350 x^{\frac {7}{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 y x^{6}-600 x^{\frac {7}{2}} y-1500 x y+8 x^{9}+120 x^{\frac {13}{2}}+600 x^{4}+1000 x^{\frac {3}{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (2 x^{3}+10 \sqrt {x}\right ) \sqrt {c_{1} -2 \ln \left (x \right )}-2 x^{3}-10 \sqrt {x}+5}{5 \sqrt {c_{1} -2 \ln \left (x \right )}-5} \\ y \left (x \right ) &= \frac {\left (2 x^{3}+10 \sqrt {x}\right ) \sqrt {c_{1} -2 \ln \left (x \right )}+2 x^{3}+10 \sqrt {x}-5}{5 \sqrt {c_{1} -2 \ln \left (x \right )}+5} \\ \end{align*}

Problem 9289

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

Problem 9290

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

Problem 9291

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

Problem 9292

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

Problem 9293

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

Problem 9294

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

Problem 9295

ODE	\[ \boxed {y^{\prime }-\frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 y a^{2} x^{2}-4 x^{2} y-8 y-y^{6} a^{2}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 y^{4} x^{2}+3 y^{2} x^{4}+x^{6}}=0} \]
program solution
Maple solution	\[ -\frac {y \left (x \right )}{\left (a -1\right ) \left (a +1\right )}+\frac {2}{\left (a^{2}-1\right )^{2} \left (a^{2} x^{2}-x^{2}-y \left (x \right )^{2}\right )^{2}}-\frac {2}{\left (a^{2}-1\right )^{2} \left (a^{2} x^{2}-x^{2}-y \left (x \right )^{2}\right )}+c_{1} = 0 \]

Problem 9296

ODE	\[ \boxed {y^{\prime }-\frac {-4 x \cos \left (x \right )+4 \sin \left (x \right ) x^{2}+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 \cos \left (2 x \right ) x^{2}+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 y^{2} x +6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+\cos \left (3 x \right ) x^{3}+15 \cos \left (x \right ) x^{3}-6 \cos \left (2 x \right ) x^{3}-10 x^{3}}{4 x}=0} \]
program solution	\[ \int _{}^{y-\frac {\left (3 \cos \left (x \right )-3+\frac {1}{x}\right ) x}{3}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\ln \left (x \right )-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\cos \left (x \right ) x +x -\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1} \right )}{9} \]

Problem 9297

ODE	\[ \boxed {y^{\prime }+\frac {8 x \left (a -1\right ) \left (a +1\right )}{8-8 y+x^{6}-2 y^{4} a^{2}-8 a^{2}+y^{6}+2 y^{4}+2 x^{4}+3 y^{2} x^{4}-y^{6} a^{2}-8 y^{2} a^{2} x^{2}+4 y^{2} x^{2}+3 y^{4} x^{2}-6 a^{2} x^{4}-2 a^{6} x^{4}+6 a^{4} x^{4}+a^{8} x^{6}-9 y^{2} a^{2} x^{4}-6 y^{4} a^{2} x^{2}-4 a^{6} x^{6}-4 a^{2} x^{6}+6 a^{4} x^{6}+4 y^{2} a^{4} x^{2}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (3 a^{2} x^{2}-3 x^{2}-2\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {5}{6}} \sqrt {3}\, \sqrt {\left (3 a^{2} x^{2}-3 x^{2}-2\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {\left (-4+\left (6 a^{2}-6\right ) x^{2}\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-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}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {\left (-4+\left (6 a^{2}-6\right ) x^{2}\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-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}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {\left (-4+\left (6 a^{2}-6\right ) x^{2}\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+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}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \sqrt {3}\, \sqrt {\left (-4+\left (6 a^{2}-6\right ) x^{2}\right ) \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+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}}{6 \left (3 \sqrt {3}+\sqrt {31}\right )^{\frac {1}{3}}} \\ \frac {4 \left (\munderset {\textit {\_R} &=\operatorname {RootOf}\left (\textit {\_Z}^{3}+2 \textit {\_Z}^{2}+8\right )}{\sum }\frac {\ln \left (-a^{2} x^{2}+x^{2}+y \left (x \right )^{2}-\textit {\_R} \right )}{\textit {\_R} \left (3 \textit {\_R} +4\right )}\right )+\left (a^{2}-1\right ) y \left (x \right )-c_{1} a^{4}+2 a^{2} c_{1} -c_{1}}{a^{4}-2 a^{2}+1} &= 0 \\ \end{align*}

Problem 9298

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

Problem 9299

ODE	\[ \boxed {y^{\prime }+\frac {1296 y}{216-1296 y-432 x y+1080 x y^{3}-2376 y^{2}-648 x^{2} y-882 y^{6}-324 y^{3} x^{2}-1944 y^{4}-1728 y^{3}+216 x^{2}+216 x^{3}+216 y^{2} x -648 y^{2} x^{2}-216 y^{4} x^{2}+216 y^{7} x -846 y^{7}+1080 y^{5} x -612 y^{5}-36 y^{11}-315 y^{9}-570 y^{8}-126 y^{10}-8 y^{12}+1152 y^{4} x +594 y^{6} x +72 x y^{8}}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -6 \left (\int _{}^{-\frac {{\mathrm e}^{4 \textit {\_Z}}}{3}-\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}}+x}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1} \right )} \]

Problem 9300

ODE	\[ \boxed {y^{\prime }+\frac {x \left (-513-432 x -378 y-456 x^{6}-540 y^{2}-594 x^{2} y-216 x^{6} y^{3}+64 x^{9}-648 y^{3} x^{2}-96 x^{8}-864 x^{4}+720 x^{3} y-144 x^{7}-216 y x^{4}-972 y^{2} x^{4}+432 x^{3} y^{2}-216 y^{3}-1134 x^{2}-756 x^{3}-576 x^{5}-1296 y^{2} x^{2}+1008 x^{5} y+432 y^{2} x^{7}-288 y x^{6}-216 y^{2} x^{6}+288 y x^{7}-648 y^{3} x^{4}+864 y^{2} x^{5}-288 y x^{8}\right )}{216 \left (x^{2}+1\right )^{4}}=0} \]
program solution	\[ \int _{}^{y-\frac {-\frac {2 x^{8}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {x^{7}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}-\frac {4 x^{6}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {9 x^{5}}{2 \left (x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1\right )}-\frac {2 x^{4}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {6 x^{3}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {5 x}{2 \left (x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1\right )}}{3 \left (\frac {x^{7}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {3 x^{5}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {3 x^{3}}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}+\frac {x}{x^{8}+4 x^{6}+6 x^{4}+4 x^{2}+1}\right )}}\frac {1}{\textit {\_a}^{3}-\frac {1}{3} \textit {\_a} +\frac {29}{27}}d \textit {\_a} -\frac {\ln \left (x^{2}+1\right )}{2}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {58 \operatorname {RootOf}\left (-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x^{2}+1\right )+6 c_{1} \right ) x^{2}+12 x^{3}-6 x^{2}+58 \operatorname {RootOf}\left (-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x^{2}+1\right )+6 c_{1} \right )-15}{18 x^{2}+18} \]