2.17.90 Problems 8901 to 9000

Problem 8901

ODE	\[ \boxed {a \cos \left (y^{\prime }\right )+b y^{\prime }=-x} \]
program solution	\[ y = \int \operatorname {RootOf}\left (a \cos \left (\textit {\_Z} \right )+\textit {\_Z} b +x \right )d x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \int \operatorname {RootOf}\left (a \cos \left (\textit {\_Z} \right )+b \textit {\_Z} +x \right )d x +c_{1} \]

Problem 8902

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

Problem 8903

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

Problem 8904

ODE	\[ \boxed {\left ({y^{\prime }}^{2}+1\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }=0} \]
program solution	\[ y = \int \tan \left (\operatorname {RootOf}\left (a x \tan \left (\textit {\_Z} \right )^{2}+\tan \left (\textit {\_Z} \right )^{2} \textit {\_Z} +a x +\tan \left (\textit {\_Z} \right )+\textit {\_Z} \right )\right )d x +c_{1} \] Warning, solution could not be verified
Maple solution	\[ y \left (x \right ) = \int \tan \left (\operatorname {RootOf}\left (a x +\sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )+\textit {\_Z} \right )\right )d x +c_{1} \]

Problem 8905

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

Problem 8906

ODE	\[ \boxed {\left (y^{\prime } x -y\right )^{n} f \left (y^{\prime }\right )+y g \left (y^{\prime }\right )+x h \left (y^{\prime }\right )=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 8907

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

Problem 8908

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

Problem 8909

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

Problem 8910

ODE	\[ \boxed {\phi \left (f \left (x , y, y^{\prime }\right ), g \left (x , y, y^{\prime }\right )\right )=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 8911

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

Problem 8912

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

Problem 8913

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

Problem 8914

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

Problem 8915

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

Problem 8916

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

Problem 8917

ODE	\[ \boxed {y^{\prime }+\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {x^{4} a}{8}+\operatorname {RootOf}\left (F \left (\textit {\_Z} \right )\right ) \\ y \left (x \right ) &= -\frac {x^{4} a}{8}+\operatorname {RootOf}\left (-x^{2}+2 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1} \right ) \\ \end{align*}

Problem 8918

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

Problem 8919

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

Problem 8920

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

Problem 8921

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

Problem 8922

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

Problem 8923

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

Problem 8924

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

Problem 8925

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

Problem 8926

ODE	\[ \boxed {y^{\prime }-\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x}=0} \]
program solution
Maple solution	\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{F \left (\textit {\_a} -\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}d \textit {\_a} -\ln \left (x \right )-c_{1} = 0 \]

Problem 8927

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

Problem 8928

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

Problem 8929

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

Problem 8930

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

Problem 8931

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

Problem 8932

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

Problem 8933

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

Problem 8934

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

Problem 8935

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

Problem 8936

ODE	\[ \boxed {y^{\prime }-\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \frac {x^{2}}{\operatorname {RootOf}\left (F \left (\textit {\_Z} \right )\right ) x^{2}+1} \\ y \left (x \right ) &= \frac {x^{2}}{\operatorname {RootOf}\left (-\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} \right ) x^{2}+1} \\ \end{align*}

Problem 8937

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

Problem 8938

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

Problem 8939

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

Problem 8940

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

Problem 8941

ODE	\[ \boxed {y^{\prime }-\frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (F \left (\textit {\_Z} \right )\right ) x^{2} \\ y \left (x \right ) &= \operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} \right ) x^{2} \\ \end{align*}

Problem 8942

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

Problem 8943

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

Problem 8944

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

Problem 8945

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

Problem 8946

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

Problem 8947

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

Problem 8948

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

Problem 8949

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

Problem 8950

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

Problem 8951

ODE	\[ \boxed {y^{\prime }-\frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (F \left (\frac {\left (\textit {\_Z} +3\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 \textit {\_Z}}\right ) \textit {\_Z} \,{\mathrm e}^{3 x^{2}}-9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} \textit {\_Z} -27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}\right ) \\ y \left (x \right ) &= -\frac {3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}}{{\mathrm e}^{\frac {3 x^{2}}{2}}-3 \operatorname {RootOf}\left (-x^{2}-18 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )-27 \textit {\_a}}d \textit {\_a} \right )+2 c_{1} \right )} \\ \end{align*}

Problem 8952

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

Problem 8953

ODE	\[ \boxed {y^{\prime }-\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )}=0} \]
program solution
Maple solution	\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {-8 \textit {\_a}^{4}-9 \textit {\_a}^{3}-12 \textit {\_a}^{2}+F \left (-\frac {1}{3} \textit {\_a}^{4}-\frac {1}{2} \textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} +x \right )-6 \textit {\_a}}{F \left (-\frac {1}{3} \textit {\_a}^{4}-\frac {1}{2} \textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} +x \right ) \textit {\_a}}d \textit {\_a} -c_{1} = 0 \]

Problem 8954

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

Problem 8955

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

Problem 8956

ODE	\[ \boxed {y^{\prime }-\frac {1}{y+2+\sqrt {3 x +1}}=0} \]
program solution	\[ \frac {\ln \left (\left (3 y+6\right ) \sqrt {3 x +1}+3 y^{2}-6 x +12 y+10\right )}{3}-\frac {2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (\sqrt {3 x +1}+2 y+4\right ) \sqrt {33}}{11 \sqrt {3 x +1}}\right )}{33} = c_{1} \] Verified OK.
Maple solution	\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (\sqrt {3 x +1}+2 y \left (x \right )+4\right ) \sqrt {33}}{11 \sqrt {3 x +1}}\right )+11 \ln \left (\left (3 y \left (x \right )+6\right ) \sqrt {3 x +1}+3 y \left (x \right )^{2}-6 x +12 y \left (x \right )+10\right )-c_{1} = 0 \]

Problem 8957

ODE	\[ \boxed {y^{\prime }-\frac {x^{2}}{y+x^{\frac {3}{2}}}=0} \]
program solution	\[ \frac {\ln \left (3 y x^{\frac {3}{2}}-2 x^{3}+3 y^{2}\right )}{3}-\frac {2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (x^{\frac {3}{2}}+2 y\right ) \sqrt {33}}{11 x^{\frac {3}{2}}}\right )}{33} = c_{1} \] Verified OK.
Maple solution	\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (x^{\frac {3}{2}}+2 y \left (x \right )\right ) \sqrt {33}}{11 x^{\frac {3}{2}}}\right )+11 \ln \left (3 y \left (x \right ) x^{\frac {3}{2}}-2 x^{3}+3 y \left (x \right )^{2}\right )-c_{1} = 0 \]

Problem 8958

ODE	\[ \boxed {y^{\prime }-\frac {x^{\frac {5}{3}}}{y+x^{\frac {4}{3}}}=0} \]
program solution	\[ \frac {9 \ln \left (x^{\frac {4}{3}}-2 y\right )}{16}+\frac {3 \ln \left (3 x^{\frac {4}{3}}+2 y\right )}{16} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{192}+12 x^{\frac {4}{3}} \textit {\_Z}^{176}+48 x^{\frac {8}{3}} \textit {\_Z}^{160}+64 x^{4} \textit {\_Z}^{144}-c_{1} \right )^{16}}{2}+\frac {x^{\frac {4}{3}}}{2} \]

Problem 8959

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

Problem 8960

ODE	\[ \boxed {y^{\prime }-\frac {x}{y+\sqrt {x^{2}+1}}=0} \]
program solution
Maple solution	\[ -\frac {2 \ln \left (11\right )}{3}+\frac {2 \ln \left (\frac {-y \left (x \right ) \sqrt {x^{2}+1}+x^{2}-y \left (x \right )^{2}+1}{\left (y \left (x \right )+\sqrt {x^{2}+1}\right )^{2}}\right )}{3}-\frac {4 \sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (3 \sqrt {x^{2}+1}+y \left (x \right )\right ) \sqrt {5}}{5 y \left (x \right )+5 \sqrt {x^{2}+1}}\right )}{15}-\frac {4 \ln \left (\frac {\sqrt {x^{2}+1}}{y \left (x \right )+\sqrt {x^{2}+1}}\right )}{3}+\frac {2 \ln \left (x^{2}+1\right )}{3}-c_{1} = 0 \]

Problem 8961

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

Problem 8962

ODE	\[ \boxed {y^{\prime }-\frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3}=0} \]
program solution	\[ \frac {\ln \left (-9 x^{4}+16 x^{2}+48 y\right )}{6}-\frac {\ln \left (3 x^{2}+4 \sqrt {x^{2}+3 y}\right )}{6}+\frac {\ln \left (-3 x^{2}+4 \sqrt {x^{2}+3 y}\right )}{6} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {x^{2}}{3}+\frac {4}{27}-\frac {4 \sqrt {x^{2}+3 y \left (x \right )}}{9} = 0 \]

Problem 8963

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

Problem 8964

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

Problem 8965

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

Problem 8966

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

Problem 8967

ODE	\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}=0} \]
program solution	\[ \frac {\ln \left (-3 \,{\mathrm e}^{\frac {4 x}{3}}+2 y \,{\mathrm e}^{\frac {2 x}{3}}+2 y^{2}\right )}{2}-\frac {x}{3}-\frac {\sqrt {7}\, \operatorname {arctanh}\left (\frac {2 \,{\mathrm e}^{-\frac {2 x}{3}} \sqrt {7}\, y}{7}+\frac {\sqrt {7}}{7}\right )}{7} = -\frac {x}{3}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-{\mathrm e}^{\operatorname {RootOf}\left (343 \operatorname {sech}\left (\frac {\left (4 c_{1} -4 x -3 \textit {\_Z} \right ) \sqrt {7}}{6}\right )^{2}+98 \,{\mathrm e}^{\textit {\_Z}}\right )}-3+2 \textit {\_Z} +2 \textit {\_Z}^{2}\right ) {\mathrm e}^{\frac {2 x}{3}} \]

Problem 8968

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

Problem 8969

ODE	\[ \boxed {y^{\prime }-\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2}=0} \]
program solution	\[ -\frac {\ln \left (9 x^{4}-4 x^{3}+24 y\right )}{24}+\frac {\ln \left (-3 x^{2}+2 \sqrt {x^{3}-6 y}\right )}{24}-\frac {\ln \left (3 x^{2}+2 \sqrt {x^{3}-6 y}\right )}{24} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} -\frac {3 x^{2}}{2}-\sqrt {x^{3}-6 y \left (x \right )} = 0 \]

Problem 8970

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

Problem 8971

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

Problem 8972

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

Problem 8973

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

Problem 8974

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

Problem 8975

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

Problem 8976

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

Problem 8977

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

Problem 8978

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

Problem 8979

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

Problem 8980

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

Problem 8981

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

Problem 8982

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

Problem 8983

ODE	\[ \boxed {y^{\prime }-x \sqrt {x^{2}-2 x +1+8 y}=-\frac {x}{4}+\frac {1}{4}} \]
program solution	\[ \frac {\ln \left (-4 x^{4}+x^{2}-2 x +8 y+1\right )}{16}-\frac {\ln \left (2 x^{2}+\sqrt {x^{2}-2 x +1+8 y}\right )}{16}+\frac {\ln \left (-2 x^{2}+\sqrt {x^{2}-2 x +1+8 y}\right )}{16} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {x^{2}}{8}+\frac {17}{128}-\frac {\sqrt {x^{2}-2 x +1+8 y \left (x \right )}}{16} = 0 \]

Problem 8984

ODE	\[ \boxed {y^{\prime }-x \sqrt {x^{2}+2 a x +a^{2}+4 y}=-\frac {x}{2}-\frac {a}{2}} \]
program solution	\[ -\frac {\ln \left (x^{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}\right )}{8}+\frac {\ln \left (-x^{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}\right )}{8}+\frac {\ln \left (-x^{4}+a^{2}+2 a x +x^{2}+4 y\right )}{8} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {a^{2}}{4}+\frac {x^{2}}{4}+\frac {1}{16}-\frac {\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )}}{4} = 0 \]

Problem 8985

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

Problem 8986

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

Problem 8987

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

Problem 8988

ODE	\[ \boxed {y^{\prime }+\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 x +3}=0} \]
program solution	\[ y = \frac {3 \ln \left (x +1\right )^{2}}{4}+\frac {9 \ln \left (x +1\right ) c_{1}}{4}+\frac {27 c_{1}^{2}}{16}-\frac {x^{2}}{3} \] Verified OK.
Maple solution	\[ c_{1} +\frac {3 \ln \left (x +1\right )}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0 \]

Problem 8989

ODE	\[ \boxed {y^{\prime }-\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}=0} \]
program solution	\[ -\frac {\ln \left (-3 y^{2} {\mathrm e}^{-\frac {4 x}{3}}+2 y \,{\mathrm e}^{-\frac {2 x}{3}}+2\right )}{2}+\frac {\sqrt {7}\, \operatorname {arctanh}\left (\frac {3 \,{\mathrm e}^{-\frac {2 x}{3}} \sqrt {7}\, y}{7}-\frac {\sqrt {7}}{7}\right )}{7}+\ln \left (y\right ) = c_{1} \] Verified OK.
Maple solution	\[ x +\frac {3 \sqrt {7}\, \operatorname {arctanh}\left (\frac {3 y \left (x \right ) \sqrt {7}\, {\mathrm e}^{-\frac {2 x}{3}}}{7}-\frac {\sqrt {7}}{7}\right )}{14}-\frac {3 \ln \left (3 y \left (x \right )^{2} {\mathrm e}^{-\frac {4 x}{3}}-2 y \left (x \right ) {\mathrm e}^{-\frac {2 x}{3}}-2\right )}{4}+\frac {3 \ln \left (y \left (x \right ) {\mathrm e}^{-\frac {2 x}{3}}\right )}{2}-c_{1} = 0 \]

Problem 8990

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

Problem 8991

ODE	\[ \boxed {y^{\prime }-x^{2} \sqrt {x^{2}-2 x +1+8 y}=-\frac {x}{4}+\frac {1}{4}} \]
program solution	\[ \frac {\ln \left (-16 x^{6}+9 x^{2}-18 x +72 y+9\right )}{12}+\frac {\ln \left (-4 x^{3}+3 \sqrt {x^{2}-2 x +1+8 y}\right )}{12}-\frac {\ln \left (4 x^{3}+3 \sqrt {x^{2}-2 x +1+8 y}\right )}{12} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {4 x^{3}}{3}-\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0 \]

Problem 8992

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

Problem 8993

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

Problem 8994

ODE	\[ \boxed {y^{\prime }-x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}=-\frac {x}{2}-\frac {a}{2}} \]
program solution	\[ \frac {\ln \left (-4 x^{6}+9 a^{2}+18 a x +9 x^{2}+36 y\right )}{6}-\frac {\ln \left (2 x^{3}+3 \sqrt {x^{2}+2 a x +a^{2}+4 y}\right )}{6}+\frac {\ln \left (-2 x^{3}+3 \sqrt {x^{2}+2 a x +a^{2}+4 y}\right )}{6} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {2 x^{3}}{3}-\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )} = 0 \]

Problem 8995

ODE	\[ \boxed {y^{\prime }-x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 y a -4 c}=-\frac {a x}{2}-\frac {b}{2}} \]
program solution	\[ \frac {\ln \left (\left (-4 x^{6}+9 x^{2}\right ) a^{2}+18 \left (x b +2 y\right ) a +9 b^{2}-36 c \right )}{6}-\frac {\ln \left (2 a \,x^{3}+3 \sqrt {a^{2} x^{2}+\left (2 x b +4 y\right ) a +b^{2}-4 c}\right )}{6}+\frac {\ln \left (-2 a \,x^{3}+3 \sqrt {a^{2} x^{2}+\left (2 x b +4 y\right ) a +b^{2}-4 c}\right )}{6} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {2 x^{3} a}{3}-\sqrt {a^{2} x^{2}+2 a x b +b^{2}+4 a y \left (x \right )-4 c} = 0 \]

Problem 8996

ODE	\[ \boxed {y^{\prime }-x^{2} \sqrt {x^{2}+2 x +1-4 y}=\frac {x}{2}+\frac {1}{2}} \]
program solution	\[ -\frac {\ln \left (4 x^{6}-9 x^{2}-18 x +36 y-9\right )}{6}-\frac {\ln \left (2 x^{3}+3 \sqrt {x^{2}+2 x +1-4 y}\right )}{6}+\frac {\ln \left (-2 x^{3}+3 \sqrt {x^{2}+2 x +1-4 y}\right )}{6} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} -\frac {2 x^{3}}{3}-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0 \]

Problem 8997

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

Problem 8998

ODE	\[ \boxed {y^{\prime }-x^{2} \sqrt {x^{2}-4 x +4 y}=-\frac {x}{2}+1} \]
program solution	\[ \frac {\ln \left (-4 x^{6}+9 x^{2}-36 x +36 y\right )}{6}-\frac {\ln \left (2 x^{3}+3 \sqrt {x^{2}-4 x +4 y}\right )}{6}+\frac {\ln \left (-2 x^{3}+3 \sqrt {x^{2}-4 x +4 y}\right )}{6} = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {2 x^{3}}{3}-\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0 \]

Problem 8999

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

Problem 9000

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