2.17.113 Problems 11201 to 11300

Problem 11201

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

Problem 11202

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

Problem 11203

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

Problem 11204

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

Problem 11205

ODE	\[ \boxed {2 y^{\prime } x -y+\ln \left (y^{\prime }\right )=0} \]
program solution	\[ y = -\infty \] Warning, solution could not be verified \[ x = -\frac {2 \left (-2 c_{1} x +\operatorname {LambertW}\left (2 x \,{\mathrm e}^{y}\right )\right ) x}{\operatorname {LambertW}\left (2 x \,{\mathrm e}^{y}\right )^{2}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -1+\sqrt {4 c_{1} x +1}-\ln \left (2\right )+\ln \left (\frac {-1+\sqrt {4 c_{1} x +1}}{x}\right ) \\ y \left (x \right ) &= -1-\sqrt {4 c_{1} x +1}-\ln \left (2\right )+\ln \left (\frac {-1-\sqrt {4 c_{1} x +1}}{x}\right ) \\ \end{align*}

Problem 11206

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

Problem 11207

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

Problem 11208

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

Problem 11209

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

Problem 11210

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

Problem 11211

ODE	\[ \boxed {y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )=-x} \]
program solution	\[ y = -i x \] Verified OK. \[ y = i x \] Verified OK. \[ y = -\frac {i \sqrt {2}\, x}{2} \] Verified OK. \[ y = \frac {i \sqrt {2}\, x}{2} \] Verified OK. \[ x = -\frac {\left (-2 {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}+2^{\frac {2}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}-2 \,2^{\frac {1}{3}} y^{2}\right ) c_{3} 2^{\frac {5}{6}} {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}} \left (-2^{\frac {1}{3}} y^{2}+{\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}\right )}{\sqrt {-\frac {2^{\frac {1}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}-2 y^{2}}{{\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}}}\, y^{3} \left (2^{\frac {1}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}-2 y^{2}\right ) \left (x -\sqrt {x^{2}+2 y^{2}}\right )} \] Warning, solution could not be verified \[ x = \frac {2^{\frac {1}{3}} c_{3} \left (4 {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}+\left (1+i \sqrt {3}\right ) 2^{\frac {2}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}+2 y^{2} \left (i \sqrt {3}-1\right ) 2^{\frac {1}{3}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}} \left (\left (\sqrt {3}+i\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}-2^{\frac {1}{3}} \left (i-\sqrt {3}\right ) y^{2}\right )}{\left (x -\sqrt {x^{2}+2 y^{2}}\right ) \sqrt {\frac {2^{\frac {1}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) \left (1+i \sqrt {3}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}+2 y^{2} \left (i \sqrt {3}-1\right )}{{\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}}}\, y^{3} \left (2^{\frac {1}{3}} \left (i-\sqrt {3}\right ) \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}-2 \left (\sqrt {3}+i\right ) y^{2}\right )} \] Warning, solution could not be verified \[ x = \frac {\left (-4 {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}+\left (i \sqrt {3}-1\right ) 2^{\frac {2}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}+2 \left (1+i \sqrt {3}\right ) y^{2} 2^{\frac {1}{3}}\right ) 2^{\frac {1}{3}} c_{3} {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}} \left ({\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}} \left (-i+\sqrt {3}\right )+y^{2} 2^{\frac {1}{3}} \left (\sqrt {3}+i\right )\right )}{\sqrt {\frac {\left (1-i \sqrt {3}\right ) 2^{\frac {1}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}}+2 \left (-i \sqrt {3}-1\right ) y^{2}}{{\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {2}{3}}}}\, y^{3} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) \left (2^{\frac {1}{3}} \left (x -\sqrt {x^{2}+2 y^{2}}\right ) {\left (\left (-x +\sqrt {x^{2}+2 y^{2}}\right ) y^{2}\right )}^{\frac {1}{3}} \left (\sqrt {3}+i\right )+2 y^{2} \left (-i+\sqrt {3}\right )\right )} \] Warning, solution could not be verified
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {i \sqrt {2}\, x}{2} \\ y \left (x \right ) &= \frac {i \sqrt {2}\, x}{2} \\ y \left (x \right ) &= \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {-2 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \textit {\_a}^{2}+2 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \textit {\_a}^{3}-{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}}+\textit {\_a} {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}}+\textit {\_a}^{2}}{{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \left (2 \textit {\_a}^{4}+3 \textit {\_a}^{2}+1\right )}d \textit {\_a} +c_{1} \right ) x \\ y \left (x \right ) &= \operatorname {RootOf}\left (-2 \ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {2 i {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \sqrt {3}\, \textit {\_a}^{2}+i {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \sqrt {3}-2 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \textit {\_a}^{2}-4 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \textit {\_a}^{3}+i \sqrt {3}\, \textit {\_a}^{2}-{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}}-2 \textit {\_a} {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}}+\textit {\_a}^{2}}{{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \left (2 \textit {\_a}^{4}+3 \textit {\_a}^{2}+1\right )}d \textit {\_a} +2 c_{1} \right ) x \\ y \left (x \right ) &= \operatorname {RootOf}\left (-2 \ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {2 i {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \sqrt {3}\, \textit {\_a}^{2}+i {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \sqrt {3}+2 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}} \textit {\_a}^{2}+4 {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \textit {\_a}^{3}+i \sqrt {3}\, \textit {\_a}^{2}+{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {2}{3}}+2 \textit {\_a} {\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}}-\textit {\_a}^{2}}{{\left (\frac {\left (\textit {\_a}^{2}-\sqrt {2 \textit {\_a}^{2}+1}+1\right ) \textit {\_a}}{\left (2 \textit {\_a}^{2}+1\right )^{\frac {3}{2}}}\right )}^{\frac {1}{3}} \left (2 \textit {\_a}^{4}+3 \textit {\_a}^{2}+1\right )}d \textit {\_a} \right )+2 c_{1} \right ) x \\ \end{align*}

Problem 11212

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

Problem 11213

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

Problem 11214

ODE	\[ \boxed {{y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}=0} \]
program solution	\[ \left (9 i 3^{\frac {2}{3}}+9 \,3^{\frac {1}{6}}\right ) \left (\int _{}^{\frac {y}{x^{3}}}-\frac {\left (3 \sqrt {3}\, \sqrt {\textit {\_a}}-\sqrt {27 \textit {\_a} -4}\right )^{\frac {1}{3}}}{\sqrt {\textit {\_a}}\, \left (-9 \left (i 3^{\frac {2}{3}}+3^{\frac {1}{6}}\right ) \sqrt {\textit {\_a}}\, \left (3 \sqrt {3}\, \sqrt {\textit {\_a}}-\sqrt {27 \textit {\_a} -4}\right )^{\frac {1}{3}}+3 \,2^{\frac {2}{3}} \left (i 3^{\frac {1}{6}}-\frac {3^{\frac {2}{3}}}{3}\right ) \left (-3 \sqrt {3}\, \sqrt {\textit {\_a}}+\sqrt {27 \textit {\_a} -4}\right )^{\frac {2}{3}}+4 \,2^{\frac {1}{3}} 3^{\frac {2}{3}}\right )}d \textit {\_a} \right )-c_{1} +3 \ln \left (x \right ) = 0 \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {4 x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (4 c_{1} x -1\right )^{2}}{64 c_{1}^{3}} \\ \end{align*}

Problem 11215

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

Problem 11216

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

Problem 11217

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

Problem 11218

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

Problem 11219

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

Problem 11220

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

Problem 11221

ODE	\[ \boxed {y-2 y^{\prime } x -y^{2} {y^{\prime }}^{3}=0} \]
program solution	\[ \frac {3 \ln \left (x \right )}{4} = \int _{}^{\frac {y}{x^{\frac {3}{4}}}}-\frac {9 \textit {\_a} \left (3 \sqrt {3}\, \textit {\_a}^{2}+\sqrt {27 \textit {\_a}^{4}+32}\right )^{\frac {1}{3}} 3^{\frac {1}{6}}}{-2 \,36^{\frac {1}{3}} {\left (\left (3 \sqrt {3}\, \textit {\_a}^{2}+\sqrt {27 \textit {\_a}^{4}+32}\right )^{2}\right )}^{\frac {1}{3}}+9 \,3^{\frac {1}{6}} \left (3 \sqrt {3}\, \textit {\_a}^{2}+\sqrt {27 \textit {\_a}^{4}+32}\right )^{\frac {1}{3}} \textit {\_a}^{2}+8 \,18^{\frac {1}{3}}}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {2 \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= \frac {2 \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= -\frac {2 i \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= \frac {2 i \left (-x^{3}\right )^{\frac {1}{4}} 6^{\frac {1}{4}}}{3} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {c_{1} \left (c_{1}^{2}+2 x \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (c_{1}^{2}+2 x \right )} \\ \end{align*}

Problem 11222

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

Problem 11223

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

Problem 11224

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

Problem 11225

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

Problem 11226

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

Problem 11227

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

Problem 11228

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

Problem 11229

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

Problem 11230

ODE	\[ \boxed {{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right )-y^{2}=0} \]
program solution	\[ y = \frac {2 c_{1} \left (\csc \left (x \right )-\cot \left (x \right )\right )^{\sqrt {\sec \left (x \right )^{2}}\, \cos \left (x \right )}}{\left (\csc \left (x \right )-\cot \left (x \right )\right ) \left (\cos \left (x \right )+1\right )} \] Verified OK. \[ y = \frac {2 c_{2} \left (\csc \left (x \right )-\cot \left (x \right )\right )^{-\sqrt {\sec \left (x \right )^{2}}\, \cos \left (x \right )}}{\left (\csc \left (x \right )-\cot \left (x \right )\right ) \left (\cos \left (x \right )+1\right )} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\operatorname {csgn}\left (\sin \left (x \right )\right ) c_{1}}{\cos \left (x \right )+\operatorname {csgn}\left (\sec \left (x \right )\right )} \\ y \left (x \right ) &= \csc \left (x \right )^{2} \left (\cos \left (x \right )+\operatorname {csgn}\left (\sec \left (x \right )\right )\right ) \operatorname {csgn}\left (\sin \left (x \right )\right ) c_{1} \\ \end{align*}

Problem 11231

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

Problem 11232

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

Problem 11233

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

Problem 11234

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

Problem 11235

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

Problem 11236

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

Problem 11237

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

Problem 11238

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

Problem 11239

ODE	\[ \boxed {8 \left (1+y^{\prime }\right )^{3}-27 \left (y+x \right ) \left (1-y^{\prime }\right )^{3}=0} \]
program solution	\[ y = -x \] Verified OK. \[ y = -x -\frac {8 {\left (2+\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}-\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}^{3}}{27 {\left (\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}-\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}^{3}} \] Warning, solution could not be verified \[ y = -x -\frac {8 {\left (2-\frac {\left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {2}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}\, \left (\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}{2}\right )}^{3}}{27 {\left (-\frac {\left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {2}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}\, \left (\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}{2}\right )}^{3}} \] Warning, solution could not be verified \[ y = -x -\frac {8 {\left (2-\frac {\left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {2}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}{2}\right )}^{3}}{27 {\left (-\frac {\left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {2}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {2 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}{9 \left (x +c_{1} \right )}+\frac {4}{3 \left (\left (6 \sqrt {3}\, \sqrt {\frac {2+27 x +27 c_{1}}{x +c_{1}}}-54\right ) \left (x +c_{1} \right )^{2}\right )^{\frac {1}{3}}}\right )}{2}\right )}^{3}} \] Warning, solution could not be verified
Maple solution	\begin{align*} y \left (x \right ) &= -x \\ \frac {x}{2}-\frac {4 \ln \left (27 y \left (x \right )+27 x +8\right )}{27}+\frac {4 \ln \left (2+3 \left (x +y \left (x \right )\right )^{\frac {1}{3}}\right )}{27}+\frac {4 \ln \left (9 \left (x +y \left (x \right )\right )^{\frac {2}{3}}-6 \left (x +y \left (x \right )\right )^{\frac {1}{3}}+4\right )}{27}-\frac {y \left (x \right )}{2}-\frac {\left (x +y \left (x \right )\right )^{\frac {2}{3}}}{2}-c_{1} &= 0 \\ \frac {x}{2}-\frac {y \left (x \right )}{2}-\frac {i \sqrt {3}\, \left (x +y \left (x \right )\right )^{\frac {2}{3}}}{4}+\frac {\left (x +y \left (x \right )\right )^{\frac {2}{3}}}{4}-c_{1} &= 0 \\ \frac {x}{2}-\frac {y \left (x \right )}{2}+\frac {i \sqrt {3}\, \left (x +y \left (x \right )\right )^{\frac {2}{3}}}{4}+\frac {\left (x +y \left (x \right )\right )^{\frac {2}{3}}}{4}-c_{1} &= 0 \\ \end{align*}

Problem 11240

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

Problem 11241

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

Problem 11242

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

Problem 11243

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }+25 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{3 x} \cos \left (4 x \right )+\frac {c_{2} {\mathrm e}^{3 x} \sin \left (4 x \right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{1} \sin \left (4 x \right )+c_{2} \cos \left (4 x \right )\right ) \]

Problem 11244

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

Problem 11245

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

Problem 11246

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

Problem 11247

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

Problem 11248

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

Problem 11249

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

Problem 11250

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

Problem 11251

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

Problem 11252

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

Problem 11253

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

Problem 11254

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x}} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+\frac {x^{3} {\mathrm e}^{-x}}{3}-\frac {x^{5} {\mathrm e}^{-x}}{60} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x} \left (x^{5}-60 c_{2} x^{2}-20 x^{3}-60 c_{3} x -60 c_{1} \right )}{60} \]

Problem 11255

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

Problem 11256

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

Problem 11257

ODE	\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y=x^{2}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x}+{\mathrm e}^{3 x} c_{3} +\frac {x^{2}}{3}+\frac {2 x}{9}+\frac {20}{27} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2}}{3}+\frac {2 x}{9}+\frac {20}{27}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{3 x} \]

Problem 11258

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

Problem 11259

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

Problem 11260

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

Problem 11261

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

Problem 11262

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

Problem 11263

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 \,{\mathrm e}^{2 x} x -\sin \left (x \right )^{2}} \]
program solution	\[ y = {\mathrm e}^{x} \left (c_{2} x +c_{1} \right )-\frac {1}{2}+2 \,{\mathrm e}^{2 x} x -4 \,{\mathrm e}^{2 x}-\frac {3 \cos \left (2 x \right )}{50}-\frac {2 \sin \left (2 x \right )}{25} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {1}{2}+2 \left (x -2\right ) {\mathrm e}^{2 x}-\frac {3 \cos \left (2 x \right )}{50}-\frac {2 \sin \left (2 x \right )}{25}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{x} \]

Problem 11264

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

Problem 11265

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

Problem 11266

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

Problem 11267

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }=3 x^{2}+\sin \left (x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} +{\mathrm e}^{3 x} c_{3} +\frac {\cos \left (x \right )}{5}+\frac {\sin \left (x \right )}{10}-\frac {14 x}{9}+\frac {2 x^{2}}{3}-\frac {x^{3}}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{3}}{3}+\frac {2 x^{2}}{3}-c_{1} {\mathrm e}^{-x}+\frac {c_{2} {\mathrm e}^{3 x}}{3}+\frac {\sin \left (x \right )}{10}+\frac {\cos \left (x \right )}{5}-\frac {14 x}{9}+c_{3} \]

Problem 11268

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

Problem 11269

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

Problem 11270

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=\cos \left (x \right )} \]
program solution	\[ y = \left (c_{2} x +c_{1} \right ) {\mathrm e}^{i x}+\left (c_{4} x +c_{3} \right ) {\mathrm e}^{-i x}+\frac {\cos \left (x \right ) \left (-4 x^{2}+2 i x +5\right )}{32}-\frac {\sin \left (x \right ) \left (i-6 x \right )}{32} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (8 c_{4} x -x^{2}+8 c_{1} +2\right ) \cos \left (x \right )}{8}+\left (\left (c_{3} +\frac {1}{8}\right ) x +c_{2} \right ) \sin \left (x \right ) \]

Problem 11271

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

Problem 11272

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y=10 x +\frac {10}{x}} \]
program solution	\[ y = \frac {c_{1}}{x}+x \left (c_{2} \cos \left (\ln \left (x \right )\right )+c_{3} \sin \left (\ln \left (x \right )\right )\right )+\frac {25 x^{2}+10 \ln \left (x \right )+8}{5 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (20-10 i\right ) \ln \left (x \right )+6-8 i+\left (2-i\right ) c_{1} \right ) \left (i \cos \left (\ln \left (x \right )\right )-\sin \left (\ln \left (x \right )\right )\right ) x^{-1-i}}{10}+\frac {\left (\left (20+10 i\right ) \ln \left (x \right )+6+8 i+\left (2+i\right ) c_{1} \right ) \left (-\sin \left (\ln \left (x \right )\right )-i \cos \left (\ln \left (x \right )\right )\right ) x^{-1+i}}{10}+\frac {5 x^{1-i} \left (i \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )\right )}{2}+\frac {5 \left (-i \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )\right ) x^{1+i}}{2}+x \left (\cos \left (\ln \left (x \right )\right ) c_{2} +\sin \left (\ln \left (x \right )\right ) c_{3} \right ) \]

Problem 11273

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

Problem 11274

ODE	\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y=x} \]
program solution	\[ y = c_{1} \left (x +1\right )^{1-i \sqrt {5}}-\frac {i c_{2} \sqrt {5}\, \left (x +1\right )^{i \sqrt {5}+1}}{10}+\frac {\left (\sqrt {5}-2 i\right ) \left (x +1\right )^{i \sqrt {5}+1}+3 i \left (x +1\right )^{1-i \sqrt {5}}+\left (-6 x -1\right ) \sqrt {5}-6 i x -i}{5 \left (-\sqrt {5}+i\right ) \left (\sqrt {5}+i\right )^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+x \right ) \sin \left (\sqrt {5}\, \ln \left (1+x \right )\right ) c_{2} +\left (1+x \right ) \cos \left (\sqrt {5}\, \ln \left (1+x \right )\right ) c_{1} +\frac {x}{5}+\frac {1}{30} \]

Problem 11275

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=\cos \left (x \right )-{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{2} +{\mathrm e}^{2 x} x +\frac {\cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+x +c_{2} \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+\frac {\cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \]

Problem 11276

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

Problem 11277

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=2 x^{3}-x \,{\mathrm e}^{3 x}} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{2} x +c_{1} \right )-\frac {x \,{\mathrm e}^{3 x}}{16}+\frac {{\mathrm e}^{3 x}}{32}-48+36 x -12 x^{2}+2 x^{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -48+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}+\frac {\left (1-2 x \right ) {\mathrm e}^{3 x}}{32}+2 x^{3}-12 x^{2}+36 x \]

Problem 11278

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=x^{2}-3 \,{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} +c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{2 x} c_{3} -\frac {3 \,{\mathrm e}^{2 x} x}{8}-\frac {x}{8}-\frac {x^{3}}{12} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (9-12 x +16 c_{1} \right ) {\mathrm e}^{2 x}}{32}-\frac {x^{3}}{12}-\frac {{\mathrm e}^{-2 x} c_{2}}{2}-\frac {x}{8}+c_{3} \]

Problem 11279

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

Problem 11280

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

Problem 11281

ODE	\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }=x^{2}-x} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{2} x +c_{1} \right )+c_{3} +\frac {x^{3}}{3}-\frac {5 x^{2}}{2}+8 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (-c_{1} x -c_{1} -c_{2} \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-\frac {5 x^{2}}{2}+8 x +c_{3} \]

Problem 11282

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

Problem 11283

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

Problem 11284

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y={\mathrm e}^{3 x}} \]
program solution	\[ y = \left (\left (c_{4} x^{2}+c_{3} x +c_{2} \right ) {\mathrm e}^{3 x}+c_{1} \right ) {\mathrm e}^{-2 x}+\frac {{\mathrm e}^{3 x}}{40} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\left (c_{3} x^{2}+c_{4} x +c_{1} \right ) {\mathrm e}^{3 x}+c_{2} +\frac {{\mathrm e}^{5 x}}{40}\right ) {\mathrm e}^{-2 x} \]

Problem 11285

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

Problem 11286

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

Problem 11287

ODE	\[ \boxed {y^{\prime \prime \prime }-y=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) x} c_{2} +{\mathrm e}^{\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) x} c_{3} -\frac {1}{2}-\frac {x \,{\mathrm e}^{x}}{3}+\frac {{\mathrm e}^{x} x^{2}}{6}-\frac {\cos \left (2 x \right )}{130}-\frac {4 \sin \left (2 x \right )}{65} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {1}{2}+c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )-\frac {\cos \left (2 x \right )}{130}-\frac {4 \sin \left (2 x \right )}{65}+\frac {\left (3 x^{2}+18 c_{1} -6 x +4\right ) {\mathrm e}^{x}}{18} \]

Problem 11288

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

Problem 11289

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

Problem 11290

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

Problem 11291

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

Problem 11292

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

Problem 11293

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

Problem 11294

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

Problem 11295

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

Problem 11296

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

Problem 11297

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

Problem 11298

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

Problem 11299

ODE	\[ \boxed {x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y=\frac {1}{x^{2}}} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {i}{2 x^{2}}}-\frac {i c_{2} {\mathrm e}^{-\frac {i}{2 x^{2}}}}{2}+\left (i {\mathrm e}^{-\frac {i}{2 x^{2}}}+{\mathrm e}^{\frac {i}{2 x^{2}}}\right ) \operatorname {undefined} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sin \left (\frac {1}{2 x^{2}}\right ) c_{2} +\cos \left (\frac {1}{2 x^{2}}\right ) c_{1} +\frac {1}{x^{2}} \]

Problem 11300

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