2.17.94 Problems 9301 to 9400

Problem 9301

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

Problem 9302

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

Problem 9303

ODE	\[ \boxed {y^{\prime }+\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 y-1296 x y-648 x y^{3}-1296 y^{2}-648 x^{2} y+2484 y^{6}-324 y^{3} x^{2}+2808 y^{4}+1728 y^{3}+216 x^{3}-1944 y^{2} x -648 y^{2} x^{2}-216 y^{4} x^{2}+216 y^{7} x +594 y^{7}+1080 y^{5} x +4428 y^{5}-36 y^{11}-315 y^{9}-18 y^{8}-126 y^{10}-8 y^{12}-432 y^{4} x +594 y^{6} x +72 x y^{8}}=0} \]
program solution
Maple solution	\begin{align*} \frac {-6 \sqrt {3 \ln \left (y \left (x \right )\right )-108 c_{1} +9}+\left (2 y \left (x \right )^{4}+3 y \left (x \right )^{3}+6 y \left (x \right )^{2}-6 x +6 y \left (x \right )\right ) \ln \left (y \left (x \right )\right )-72 y \left (x \right )^{4} c_{1} -108 c_{1} y \left (x \right )^{3}-216 c_{1} y \left (x \right )^{2}+216 c_{1} x -216 c_{1} y \left (x \right )+18}{216 c_{1} -6 \ln \left (y \left (x \right )\right )} &= 0 \\ \frac {6 \sqrt {3 \ln \left (y \left (x \right )\right )-108 c_{1} +9}+\left (2 y \left (x \right )^{4}+3 y \left (x \right )^{3}+6 y \left (x \right )^{2}-6 x +6 y \left (x \right )\right ) \ln \left (y \left (x \right )\right )-72 y \left (x \right )^{4} c_{1} -108 c_{1} y \left (x \right )^{3}-216 c_{1} y \left (x \right )^{2}+216 c_{1} x -216 c_{1} y \left (x \right )+18}{216 c_{1} -6 \ln \left (y \left (x \right )\right )} &= 0 \\ \end{align*}

Problem 9304

ODE	\[ \boxed {y^{\prime }-\frac {\left (x y+1\right )^{3}}{x^{5}}=0} \]
program solution	\[ \frac {\ln \left (y-\frac {1}{x}-1\right )}{3}-\frac {\ln \left (\left (y-\frac {1}{x}\right )^{2}+y-\frac {1}{x}+1\right )}{6}-\frac {\sqrt {3}\, \arctan \left (\frac {\left (2 y-\frac {2}{x}+1\right ) \sqrt {3}}{3}\right )}{3}+\frac {1}{x}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-2+x^{3} \left (\tan \left (\operatorname {RootOf}\left (18 x^{3} \left (-\frac {1}{x^{6}}\right )^{\frac {2}{3}}+6 \textit {\_Z} \sqrt {3}-3 \ln \left (3\right )+\ln \left (\left (\sqrt {3}\, \sin \left (\textit {\_Z} \right )+3 \cos \left (\textit {\_Z} \right )\right )^{6}\right )-18 c_{1} \right )\right ) \sqrt {3}+1\right ) \left (-\frac {1}{x^{6}}\right )^{\frac {1}{3}}}{2 x} \]

Problem 9305

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

Problem 9306

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

Problem 9307

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

Problem 9308

ODE	\[ \boxed {y^{\prime }-y^{3}-y^{2} x^{2}-\frac {y x^{4}}{3}=\frac {1}{27} x^{6}-\frac {2}{3} x} \]
program solution	\[ y = \frac {1}{\sqrt {-2 c_{2} -2 x}}-x^{2} \] Verified OK. \[ y = -\frac {1}{\sqrt {-2 c_{2} -2 x}}-x^{2} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {x^{2} \sqrt {-54 c_{1} -2 x}-3}{3 \sqrt {-54 c_{1} -2 x}} \\ y \left (x \right ) &= -\frac {x^{2} \sqrt {-54 c_{1} -2 x}+3}{3 \sqrt {-54 c_{1} -2 x}} \\ \end{align*}

Problem 9309

ODE	\[ \boxed {y^{\prime }-\frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x}=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (3\right )-\sqrt {3}\, \ln \left (-\frac {1}{-2+\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+\cos \left (2 \textit {\_Z} \right )}\right )+\sqrt {3}\, \ln \left (7\right )+3 \sqrt {3}\, c_{1} -2 \sqrt {3}\, x -2 \textit {\_Z} \right )\right )-1}{2 x^{3}} \]

Problem 9310

ODE	\[ \boxed {y^{\prime }-y \left (y^{2}+{\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {\left (\sqrt {11}\, \tan \left (\operatorname {RootOf}\left (-4 \sqrt {11}\, x^{2}-8 \sqrt {11}\, \ln \left (11\right )-4 \sqrt {11}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} {\mathrm e}^{2 x^{2}}\right )+8 \sqrt {11}\, \ln \left (5\right )+8 \sqrt {11}\, \ln \left (-\sqrt {11}+11 \tan \left (\textit {\_Z} \right )\right )+9 \sqrt {11}\, c_{1} -8 \textit {\_Z} \right )\right )-1\right ) {\mathrm e}^{-x^{2}}}{2} \]

Problem 9311

ODE	\[ \boxed {y^{\prime }-\frac {y \left (y^{2}+x y+x^{2}+x \right )}{x^{2}}=0} \]
program solution	\[ 27 \left (\int _{}^{\frac {y-\frac {x}{3}}{x}}\frac {1}{27 \textit {\_a}^{3}+18 \textit {\_a} -7}d \textit {\_a} \right ) = x +c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x \left (\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (2 \sqrt {3}\, \ln \left (3\right )-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (-\sqrt {3}+3 \tan \left (\textit {\_Z} \right )\right )+2 \sqrt {3}\, c_{1} +2 \sqrt {3}\, x +2 \textit {\_Z} \right )\right )-1\right )}{2} \]

Problem 9312

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

Problem 9313

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

Problem 9314

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

Problem 9315

ODE	\[ \boxed {y^{\prime }-\frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2}=0} \]
program solution	\[ \frac {\sqrt {3}\, \arctan \left (\frac {2 \,{\mathrm e}^{-\frac {x^{2}}{4}} \sqrt {3}\, y}{3}+\frac {\sqrt {3}}{3}\right )}{6}+\frac {\ln \left ({\mathrm e}^{\frac {x^{2}}{2}}+y \,{\mathrm e}^{\frac {x^{2}}{4}}+y^{2}\right )}{4}-\frac {\ln \left (y\right )}{2} = -\frac {x}{2}+c_{1} \] Verified OK.
Maple solution	\[ -\frac {\ln \left (7\right )}{3}+\frac {\ln \left (1+y \left (x \right )^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{4}}\right )}{3}+\frac {2 \sqrt {3}\, \arctan \left (\frac {2 y \left (x \right ) \sqrt {3}\, {\mathrm e}^{-\frac {x^{2}}{4}}}{3}+\frac {\sqrt {3}}{3}\right )}{9}-\frac {2 \ln \left (y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{4}}\right )}{3}+\frac {2 x}{3}-c_{1} = 0 \]

Problem 9316

ODE	\[ \boxed {y^{\prime }-\frac {y^{3}-3 y^{2} x +3 y x^{2}-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )}=0} \]
program solution	\[ \frac {\ln \left (y+x +1\right )}{3}-\frac {\ln \left (\left (y+x \right )^{2}-y-x +1\right )}{6}+\frac {\sqrt {3}\, \arctan \left (\frac {2 \left (-\frac {1}{2}+y+x \right ) \sqrt {3}}{3}\right )}{3}+\operatorname {arctanh}\left (x \right )-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{2}-1\right ) \left (\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (9 \ln \left (\frac {x +1}{x -1}\right ) \left (\frac {1}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )^{\frac {2}{3}} x^{4}-18 \ln \left (\frac {x +1}{x -1}\right ) \left (\frac {1}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )^{\frac {2}{3}} x^{2}+9 \ln \left (\frac {x +1}{x -1}\right ) \left (\frac {1}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )^{\frac {2}{3}}+6 \textit {\_Z} \sqrt {3}+2 \ln \left (\frac {\left (\tan \left (\textit {\_Z} \right )+\sqrt {3}\right )^{3}}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )+3 \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \ln \left (\frac {1}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )-18 c_{1} \right )\right )+1\right ) \left (\frac {1}{\left (x +1\right )^{3} \left (x -1\right )^{3}}\right )^{\frac {1}{3}}}{2}+x \]

Problem 9317

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

Problem 9318

ODE	\[ \boxed {y^{\prime }-\frac {\left (x y+1\right ) \left (x^{2} y^{2}+y x^{2}+2 x y+1+x +x^{2}\right )}{x^{5}}=0} \]
program solution	\[ \int _{}^{y-\frac {\left (\frac {1}{x^{2}}+\frac {3}{x^{3}}\right ) x^{2}}{3}}\frac {1}{\textit {\_a}^{3}+\frac {2}{3} \textit {\_a} -\frac {34}{27}}d \textit {\_a} +\frac {1}{x}-c_{2} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {17 \operatorname {RootOf}\left (162 \left (\int _{}^{\textit {\_Z}}\frac {1}{289 \textit {\_a}^{3}+54 \textit {\_a} -54}d \textit {\_a} \right ) x +3 c_{1} x +2\right ) x -3 x -9}{9 x} \]

Problem 9319

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

Problem 9320

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

Problem 9321

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

Problem 9322

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

Problem 9323

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

Problem 9324

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

Problem 9325

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

Problem 9326

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

Problem 9327

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

Problem 9328

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

Problem 9329

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

Problem 9330

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

Problem 9331

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

Problem 9332

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

Problem 9333

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

Problem 9334

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

Problem 9335

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

Problem 9336

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

Problem 9337

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

Problem 9338

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

Problem 9339

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

Problem 9340

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

Problem 9341

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

Problem 9342

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

Problem 9343

ODE	\[ \boxed {y^{\prime \prime }+\left (x a +b \right ) y=0} \]
program solution	\[ y = -c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \sqrt {x}\right )-c_{2} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \sqrt {x}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \operatorname {AiryAi}\left (-\frac {a x +b}{a^{\frac {2}{3}}}\right )+c_{2} \operatorname {AiryBi}\left (-\frac {a x +b}{a^{\frac {2}{3}}}\right ) \]

Problem 9344

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

Problem 9345

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

Problem 9346

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

Problem 9347

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

Problem 9348

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

Problem 9349

ODE	\[ \boxed {y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y=0} \]
program solution	\[ y = -c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \sqrt {x}\right )-c_{2} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \sqrt {x}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{-\frac {c}{2}} \left (c_{1} \operatorname {WhittakerM}\left (-\frac {i b}{\sqrt {a}\, \left (2 c +2\right )}, \frac {1}{2 c +2}, \frac {2 i \sqrt {a}\, x^{c} x}{c +1}\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {i b}{\sqrt {a}\, \left (2 c +2\right )}, \frac {1}{2 c +2}, \frac {2 i \sqrt {a}\, x^{c} x}{c +1}\right )\right ) \]

Problem 9350

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

Problem 9351

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

Problem 9352

ODE	\[ \boxed {y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9353

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

Problem 9354

ODE	\[ \boxed {y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = c_{1} \operatorname {MathieuC}\left (-\frac {a}{2}-b , \frac {a}{4}, i x \right )+c_{2} \operatorname {MathieuS}\left (-\frac {a}{2}-b , \frac {a}{4}, i x \right ) \]

Problem 9355

ODE	\[ \boxed {y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = c_{1} \operatorname {MathieuC}\left (b , -\frac {a}{2}, x\right )+c_{2} \operatorname {MathieuS}\left (b , -\frac {a}{2}, x\right ) \]

Problem 9356

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

Problem 9357

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

Problem 9358

ODE	\[ \boxed {y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (-1+n \right )}{\sin \left (x \right )^{2}}+a \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \sin \left (x \right )^{n} \left (c_{1} \cos \left (x \right )^{m} \operatorname {hypergeom}\left (\left [\frac {n}{2}+\frac {m}{2}+\frac {i \sqrt {a}}{2}, \frac {n}{2}+\frac {m}{2}-\frac {i \sqrt {a}}{2}\right ], \left [\frac {1}{2}+m \right ], \cos \left (x \right )^{2}\right )+c_{2} \cos \left (x \right )^{-m +1} \operatorname {hypergeom}\left (\left [\frac {n}{2}-\frac {m}{2}+\frac {i \sqrt {a}}{2}+\frac {1}{2}, \frac {n}{2}-\frac {m}{2}-\frac {i \sqrt {a}}{2}+\frac {1}{2}\right ], \left [\frac {3}{2}-m \right ], \cos \left (x \right )^{2}\right )\right ) \]

Problem 9359

ODE	\[ \boxed {y^{\prime \prime }-\left (n \left (1+n \right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9360

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

Problem 9361

ODE	\[ \boxed {y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 9362

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

Problem 9363

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

Problem 9364

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

Problem 9365

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

Problem 9366

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

Problem 9367

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

Problem 9368

ODE	\[ \boxed {y^{\prime \prime }+a y^{\prime }+y b=f \left (x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}-\frac {c_{2} {\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}}{\sqrt {a^{2}-4 b}}+\frac {\left (\int _{0}^{x}f \left (\alpha \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) \alpha }{2}}d \alpha \right ) {\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}-\left (\int _{0}^{x}f \left (\alpha \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) \alpha }{2}}d \alpha \right ) {\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}}{\sqrt {a^{2}-4 b}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}} \left (\int f \left (x \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right )+{\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}} c_{2} \sqrt {a^{2}-4 b}-{\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}} \left (-\sqrt {a^{2}-4 b}\, c_{1} +\int f \left (x \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right )}{\sqrt {a^{2}-4 b}} \]

Problem 9369

ODE	\[ \boxed {y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\frac {x \left (b x +a \right )}{2}} x \left (\operatorname {KummerU}\left (\frac {a^{2}+12 b +4 c}{16 b}, \frac {3}{2}, b \,x^{2}\right ) c_{2} +\operatorname {KummerM}\left (\frac {a^{2}+12 b +4 c}{16 b}, \frac {3}{2}, b \,x^{2}\right ) c_{1} \right ) \]

Problem 9370

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

Problem 9371

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

Problem 9372

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

Problem 9373

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

Problem 9374

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

Problem 9375

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

Problem 9376

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

Problem 9377

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

Problem 9378

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

Problem 9379

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

Problem 9380

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

Problem 9381

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

Problem 9382

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

Problem 9383

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

Problem 9384

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

Problem 9385

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

Problem 9386

ODE	\[ \boxed {y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (c x +d \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\frac {c x}{a}} \left (\operatorname {KummerM}\left (\frac {a^{2} d -a c b +c^{2}}{2 a^{3}}, \frac {1}{2}, -\frac {\left (a^{2} x +a b -2 c \right )^{2}}{2 a^{3}}\right ) c_{1} +\operatorname {KummerU}\left (\frac {a^{2} d -a c b +c^{2}}{2 a^{3}}, \frac {1}{2}, -\frac {\left (a^{2} x +a b -2 c \right )^{2}}{2 a^{3}}\right ) c_{2} \right ) \]

Problem 9387

ODE	\[ \boxed {y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \left (c_{2} \left (a^{2} x +a b -4 \operatorname {a1} x -2 \operatorname {b1} \right ) \operatorname {hypergeom}\left (\left [\frac {3 \left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}+a^{3}-2 a^{2} \operatorname {c1} +2 \left (\operatorname {b1} b -2 \operatorname {a1} \right ) a +2 \left (-b^{2}+4 \operatorname {c1} \right ) \operatorname {a1} -2 \operatorname {b1}^{2}}{4 \left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}}\right ], \left [\frac {3}{2}\right ], \frac {\left (a^{2} x +a b -4 \operatorname {a1} x -2 \operatorname {b1} \right )^{2}}{2 \left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}}\right )+\operatorname {hypergeom}\left (\left [\frac {\left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}+a^{3}-2 a^{2} \operatorname {c1} +\left (2 \operatorname {b1} b -4 \operatorname {a1} \right ) a +\left (-2 b^{2}+8 \operatorname {c1} \right ) \operatorname {a1} -2 \operatorname {b1}^{2}}{4 \left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}}\right ], \left [\frac {1}{2}\right ], \frac {\left (a^{2} x +a b -4 \operatorname {a1} x -2 \operatorname {b1} \right )^{2}}{2 \left (a^{2}-4 \operatorname {a1} \right )^{\frac {3}{2}}}\right ) c_{1} \right ) {\mathrm e}^{-\frac {x \left (\left (a x +2 b \right ) \sqrt {a^{2}-4 \operatorname {a1}}+x \left (a^{2}-4 \operatorname {a1} \right )+2 a b -4 \operatorname {b1} \right )}{4 \sqrt {a^{2}-4 \operatorname {a1}}}} \]

Problem 9388

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

Problem 9389

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

Problem 9390

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

Problem 9391

ODE	\[ \boxed {y^{\prime \prime }+x^{4} y^{\prime }-y x^{3}=0} \]
program solution	\[ y = c_{1} x +c_{2} x \left (\int \frac {{\mathrm e}^{-\frac {x^{5}}{5}}}{x^{2}}d x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {9 \,{\mathrm e}^{-\frac {x^{5}}{5}} \left (\frac {25 c_{2} x^{5} \operatorname {WhittakerM}\left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right ) {\mathrm e}^{\frac {x^{5}}{10}}}{9}+\frac {25 c_{1} x^{3} {\mathrm e}^{\frac {x^{5}}{5}}}{9}+5^{\frac {3}{5}} c_{2} \left (x^{5}\right )^{\frac {2}{5}} \left (x^{5}+4\right )\right )}{25 x^{2}} \]

Problem 9392

ODE	\[ \boxed {y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\frac {a \,x^{q}}{q}} x \left (\operatorname {KummerM}\left (1-\frac {b}{a q}, 1+\frac {1}{q}, \frac {a \,x^{q}}{q}\right ) c_{1} +\operatorname {KummerU}\left (1-\frac {b}{a q}, 1+\frac {1}{q}, \frac {a \,x^{q}}{q}\right ) c_{2} \right ) \]

Problem 9393

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

Problem 9394

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

Problem 9395

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

Problem 9396

ODE	\[ \boxed {y^{\prime \prime }+a y^{\prime }+y b=-\tan \left (x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}-\frac {c_{2} {\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}}{\sqrt {a^{2}-4 b}}+\frac {-\left (\int _{0}^{x}\tan \left (\alpha \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) \alpha }{2}}d \alpha \right ) {\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}+\left (\int _{0}^{x}\tan \left (\alpha \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) \alpha }{2}}d \alpha \right ) {\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}}{\sqrt {a^{2}-4 b}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-{\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}} \left (\int \tan \left (x \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right )+{\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}} \left (\int \tan \left (x \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right )+{\mathrm e}^{\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}} c_{2} \sqrt {a^{2}-4 b}+{\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}} c_{1} \sqrt {a^{2}-4 b}}{\sqrt {a^{2}-4 b}} \]

Problem 9397

ODE	\[ \boxed {y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \sin \left (x \right )^{-n +\frac {1}{2}} \left (c_{1} \operatorname {LegendreP}\left (-\frac {1}{2}+\sqrt {-a^{2}+2 n^{2}}, n -\frac {1}{2}, \cos \left (x \right )\right )+c_{2} \operatorname {LegendreQ}\left (-\frac {1}{2}+\sqrt {-a^{2}+2 n^{2}}, n -\frac {1}{2}, \cos \left (x \right )\right )\right ) \]

Problem 9398

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )+y \cos \left (x \right )^{2}=0} \]
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 9399

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

Problem 9400

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