2.17.72 Problems 7101 to 7200

Problem 7101

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

Problem 7102

ODE	\[ \boxed {y^{\prime }+4 \sin \left (-y+x \right )=-4} \]
program solution	\[ \text {Expression too large to display} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x +2 \arctan \left (\frac {3 \tan \left (-\frac {3 x}{2}+\frac {3 c_{1}}{2}\right )}{5}+\frac {4}{5}\right ) \]

Problem 7103

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

Problem 7104

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

Problem 7105

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

Problem 7106

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

Problem 7107

ODE	\[ \boxed {y y^{\prime \prime }=x} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7108

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

Problem 7109

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

Problem 7110

ODE	\[ \boxed {3 y y^{\prime \prime }=\sin \left (x \right )} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7111

ODE	\[ \boxed {3 y y^{\prime \prime }+y=5} \]
program solution	\[ \int _{}^{y}\frac {3}{\sqrt {-6 \textit {\_a} +30 \ln \left (\textit {\_a} \right )+18 c_{1}}}d \textit {\_a} = x +c_{2} \] Verified OK. \[ \int _{}^{y}-\frac {3}{\sqrt {-6 \textit {\_a} +30 \ln \left (\textit {\_a} \right )+18 c_{1}}}d \textit {\_a} = x +c_{3} \] Verified OK.
Maple solution	\begin{align*} -3 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1} -6 \textit {\_a}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ 3 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1} -6 \textit {\_a}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*}

Problem 7112

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

Problem 7113

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

Problem 7114

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

Problem 7115

ODE	\begin {align*} x^{\prime }\left (t \right )&=9 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )-y \left (t \right )\\ z^{\prime }\left (t \right )&=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t} \\ y \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{3 t}}{2}-c_{3} {\mathrm e}^{5 t} \\ z \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t}+c_{1} {\mathrm e}^{3 t} \\ \end{align*}

Problem 7116

ODE	\begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+7 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{4 t} \left (3 c_{2} t +3 c_{1} +c_{2} \right )}{3} \\ \end{align*}

Problem 7117

ODE	\begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+5 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \\ \end{align*}

Problem 7118

ODE	\begin {align*} x^{\prime }\left (t \right )&=7 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )+3 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -{\mathrm e}^{5 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right ) \\ \end{align*}

Problem 7119

ODE	\begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=y \left (t \right )\\ z^{\prime }\left (t \right )&=z \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ z \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ \end{align*}

Problem 7120

ODE	\begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )-z \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= -{\mathrm e}^{2 t} \left (2 c_{3} t +c_{2} -4 c_{3} \right ) \\ y \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ z \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +c_{1} +2 c_{3} \right ) \\ \end{align*}

Problem 7121

ODE	\[ \boxed {x^{\prime }-4 A k \left (\frac {x}{A}\right )^{\frac {3}{4}}+3 k x=0} \]
program solution	\[ -\frac {4 \ln \left (3 \left (\frac {x}{A}\right )^{\frac {1}{4}}-4\right )}{3 k} = t +c_{1} \] Verified OK.
Maple solution	\[ \frac {\ln \left (9 \sqrt {\frac {x \left (t \right )}{A}}-16\right )-\ln \left (9 \sqrt {\frac {x \left (t \right )}{A}}+16\right )+2 \ln \left (3 \left (\frac {x \left (t \right )}{A}\right )^{\frac {1}{4}}-4\right )-2 \ln \left (3 \left (\frac {x \left (t \right )}{A}\right )^{\frac {1}{4}}+4\right )+\ln \left (256 A -81 x \left (t \right )\right )+\left (3 t +3 c_{1} \right ) k}{3 k} = 0 \]

Problem 7122

ODE	\[ \boxed {\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}=-x} \]
program solution	\[ y = -i x \] Verified OK. \[ y = i x \] Verified OK. \[ y = \frac {-\sqrt {-\frac {c_{2}^{2} x^{2}}{c_{2}^{2} x^{2}-1}+1}-2}{2 c_{2} \sqrt {-\frac {1}{c_{2}^{2} x^{2}-1}}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-x^{2}+c_{1}}\, \left (2+\sqrt {\frac {c_{1}}{-x^{2}+c_{1}}}\right )}{2} \\ y \left (x \right ) &= \frac {\sqrt {-x^{2}+c_{1}}\, \left (2+\sqrt {\frac {c_{1}}{-x^{2}+c_{1}}}\right )}{2} \\ y \left (x \right ) &= -\frac {\sqrt {-9 x^{2}+15 c_{1} -6 \sqrt {-3 c_{1} x^{2}+4 c_{1}^{2}}}}{3} \\ y \left (x \right ) &= \frac {\sqrt {-9 x^{2}+15 c_{1} -6 \sqrt {-3 c_{1} x^{2}+4 c_{1}^{2}}}}{3} \\ y \left (x \right ) &= -\frac {\sqrt {-9 x^{2}+15 c_{1} +6 \sqrt {-3 c_{1} x^{2}+4 c_{1}^{2}}}}{3} \\ y \left (x \right ) &= \frac {\sqrt {-9 x^{2}+15 c_{1} +6 \sqrt {-3 c_{1} x^{2}+4 c_{1}^{2}}}}{3} \\ \end{align*}

Problem 7123

ODE	\[ \boxed {\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}=-x} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
program solution	\[ y = -i x \] Warning, solution could not be verified \[ y = i x \] Warning, solution could not be verified \[ y = \frac {\sqrt {-\frac {1}{x^{2}-4}}+1}{\sqrt {-\frac {1}{x^{2}-4}}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -3+\sqrt {-x^{2}+36} \\ y \left (x \right ) &= 1+\sqrt {-x^{2}+4} \\ \end{align*}

Problem 7124

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

Problem 7125

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

Problem 7126

ODE	\[ \boxed {y^{\prime }-2 \sqrt {y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ y = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = 0 \]

Problem 7127

ODE	\[ \boxed {z^{\prime \prime }+3 z^{\prime }+2 z=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}} \]
program solution	\[ z = c_{1} {\mathrm e}^{-2 t}+{\mathrm e}^{-t} c_{2} -4 \,{\mathrm e}^{-4 t}+12 \,{\mathrm e}^{-3 t} \] Verified OK.
Maple solution	\[ z \left (t \right ) = \left (-{\mathrm e}^{-t} c_{1} -4 \,{\mathrm e}^{-3 t}+12 \,{\mathrm e}^{-2 t}+c_{2} \right ) {\mathrm e}^{-t} \]

Problem 7128

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

Problem 7129

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

Problem 7130

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

Problem 7131

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

Problem 7132

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

Problem 7133

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

Problem 7134

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

Problem 7135

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime } y=2 x} \]
program solution	\[ y = \frac {\left (i c_{1} \sqrt {2}-6\right ) c_{4} \operatorname {WhittakerM}\left (-\frac {i c_{1} \sqrt {2}}{8}+1, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+8 \operatorname {WhittakerW}\left (-\frac {i c_{1} \sqrt {2}}{8}+1, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+c_{4} \left (2+i \left (-2 x^{2}-c_{1} \right ) \sqrt {2}\right ) \operatorname {WhittakerM}\left (-\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+\operatorname {WhittakerW}\left (-\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right ) \left (2+i \left (-2 x^{2}-c_{1} \right ) \sqrt {2}\right )}{2 x \left (c_{4} \operatorname {WhittakerM}\left (-\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+\operatorname {WhittakerW}\left (-\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\operatorname {WhittakerM}\left (\frac {i c_{1} \sqrt {2}}{8}+1, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right ) \left (6+i c_{1} \sqrt {2}\right )+8 c_{2} \operatorname {WhittakerW}\left (\frac {i c_{1} \sqrt {2}}{8}+1, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+2 \left (1-i \left (x^{2}-\frac {c_{1}}{2}\right ) \sqrt {2}\right ) \left (c_{2} \operatorname {WhittakerW}\left (\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+\operatorname {WhittakerM}\left (\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )\right )}{2 x \left (c_{2} \operatorname {WhittakerW}\left (\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+\operatorname {WhittakerM}\left (\frac {i c_{1} \sqrt {2}}{8}, \frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )\right )} \]

Problem 7136

ODE	\[ \boxed {y^{\prime }-y^{2}=x^{2}+x} \]
program solution	\[ y = \frac {\left (4 i x^{2}+4 i x +i-4\right ) \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right )+4 \left (\left (-\frac {1}{12}-i\right ) \left (x +\frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {7}{4}-\frac {i}{16}\right ], \left [\frac {5}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right )+\frac {\left (\left (-\frac {1}{4}-i\right ) \operatorname {hypergeom}\left (\left [\frac {5}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right )+i \operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right )\right ) c_{3}}{2}\right ) \left (x +\frac {1}{2}\right )}{2 \left (1+2 x \right ) \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right )+2 \operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (1+2 x \right )^{2}}{4}\right ) c_{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 \left (i x^{2}+i x -1+\frac {1}{4} i\right ) c_{1} \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+2 \left (\left (-\frac {1}{12}-i\right ) c_{1} \left (x +\frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {7}{4}-\frac {i}{16}\right ], \left [\frac {5}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\left (-\frac {1}{8}-\frac {i}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {5}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\frac {i \operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )}{2}\right ) \left (x +\frac {1}{2}\right )}{\left (2 x +1\right ) c_{1} \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )} \]

Problem 7137

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

Problem 7138

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

Problem 7139

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

Problem 7140

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

Problem 7141

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

Problem 7142

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

Problem 7143

ODE	\[ \boxed {y^{\prime \prime }-x y^{\prime }-y x=x^{5}-24} \]
program solution	\[ y = -\frac {i {\mathrm e}^{-2-x} \left (x +2\right ) c_{2} \sqrt {2}\, \sqrt {\pi }\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right )}{2}-c_{2} {\mathrm e}^{\frac {x \left (x +2\right )}{2}}+c_{1} \left (x +2\right ) {\mathrm e}^{-x}+\frac {\left (\int _{0}^{x}\left (\alpha ^{5}-24\right ) \left (i \sqrt {2}\, \left (\alpha +2\right ) {\mathrm e}^{-2} \sqrt {\pi }\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (\alpha +2\right )}{2}\right )+2 \,{\mathrm e}^{\frac {\alpha \left (\alpha +4\right )}{2}}\right ) {\mathrm e}^{-\frac {\alpha \left (\alpha +2\right )}{2}}d \alpha \right ) \left (x +2\right ) {\mathrm e}^{-x}}{2}+\frac {\left (2+i \left (x +2\right ) \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) \sqrt {2}\, \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (x +2\right )^{2}}{2}}\right ) \left (x^{5}+x^{4}+4 x^{3}+12 x -36\right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \pi \,{\mathrm e}^{-2-x} c_{1} \left (x +2\right ) \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right )-i \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{\frac {x \left (x +2\right )}{2}} c_{1} +{\mathrm e}^{-x} \left (x +2\right ) c_{2} -x^{4}+4 x^{3}-12 x^{2}+12 x +12 \]

Problem 7144

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

Problem 7145

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

Problem 7146

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

Problem 7147

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

Problem 7148

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

Problem 7149

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

Problem 7150

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

Problem 7151

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

Problem 7152

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

Problem 7153

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

Problem 7154

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

Problem 7155

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

Problem 7156

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

Problem 7157

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

Problem 7158

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

Problem 7159

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

Problem 7160

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }-y x=x^{3}-2} \]
program solution	\[ y = \pi \left (-\left (\int _{0}^{x}\operatorname {AiryBi}\left (\alpha +4\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryAi}\left (x +4\right )+\left (\int _{0}^{x}\operatorname {AiryAi}\left (\alpha +4\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryBi}\left (x +4\right )\right )+{\mathrm e}^{2 x} \left (c_{1} \operatorname {AiryAi}\left (x +4\right )+c_{2} \operatorname {AiryBi}\left (x +4\right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \operatorname {AiryAi}\left (x +4\right ) c_{2} +{\mathrm e}^{2 x} \operatorname {AiryBi}\left (x +4\right ) c_{1} -x^{2}+8 \]

Problem 7161

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }-y x=x^{3}-2} \]
program solution	\[ y = \pi \left (-\left (\int _{0}^{x}\operatorname {AiryBi}\left (\alpha +9\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryAi}\left (x +9\right )+\left (\int _{0}^{x}\operatorname {AiryAi}\left (\alpha +9\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryBi}\left (x +9\right )\right )+{\mathrm e}^{3 x} \left (c_{1} \operatorname {AiryAi}\left (x +9\right )+c_{2} \operatorname {AiryBi}\left (x +9\right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{3 x} \operatorname {AiryAi}\left (9+x \right ) c_{2} +{\mathrm e}^{3 x} \operatorname {AiryBi}\left (9+x \right ) c_{1} -x^{2}+12 \]

Problem 7162

ODE	\[ \boxed {y^{\prime \prime }-8 y^{\prime }-y x=x^{3}-2} \]
program solution	\[ y = \pi \left (-\left (\int _{0}^{x}\operatorname {AiryBi}\left (\alpha +16\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryAi}\left (x +16\right )+\left (\int _{0}^{x}\operatorname {AiryAi}\left (\alpha +16\right ) \left (\alpha ^{3}-2\right )d \alpha \right ) \operatorname {AiryBi}\left (x +16\right )\right )+{\mathrm e}^{4 x} \left (c_{1} \operatorname {AiryAi}\left (x +16\right )+c_{2} \operatorname {AiryBi}\left (x +16\right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{4 x} \operatorname {AiryAi}\left (16+x \right ) c_{2} +{\mathrm e}^{4 x} \operatorname {AiryBi}\left (16+x \right ) c_{1} -x^{2}+16 \]

Problem 7163

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

Problem 7164

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

Problem 7165

ODE	\[ \boxed {y^{\prime \prime }-y x=x^{3}-2} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\frac {x \left (\frac {20 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )}{3}+x \left (-5 \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right ) \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right )+x^{2} \left (-\frac {5 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right )}{6}+x \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right )\right )\right )\right )}{10 \Gamma \left (\frac {2}{3}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -x^{2} \]

Problem 7166

ODE	\[ \boxed {y^{\prime \prime }-y x=x^{6}-64} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\frac {x \left (-\frac {16 x^{6} \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {7}{3}\right ], \left [\frac {2}{3}, \frac {10}{3}\right ], \frac {x^{3}}{9}\right )}{21}+x^{7} \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right ) \operatorname {hypergeom}\left (\left [\frac {8}{3}\right ], \left [\frac {4}{3}, \frac {11}{3}\right ], \frac {x^{3}}{9}\right )+\frac {1024 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )}{3}-256 x \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right ) \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right )\right )}{16 \Gamma \left (\frac {2}{3}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {16 x^{7} \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {7}{3}\right ], \left [\frac {2}{3}, \frac {10}{3}\right ], \frac {x^{3}}{9}\right )-21 x^{8} \Gamma \left (\frac {2}{3}\right )^{2} \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {8}{3}\right ], \left [\frac {4}{3}, \frac {11}{3}\right ], \frac {x^{3}}{9}\right )-7168 x \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )+5376 \Gamma \left (\frac {2}{3}\right ) \left (x^{2} \Gamma \left (\frac {2}{3}\right ) \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right )+\frac {\operatorname {AiryBi}\left (x \right ) c_{1}}{16}+\frac {\operatorname {AiryAi}\left (x \right ) c_{2}}{16}\right )}{336 \Gamma \left (\frac {2}{3}\right )} \]

Problem 7167

ODE	\[ \boxed {y^{\prime \prime }-y x=x} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\pi \left (\int _{0}^{x}\operatorname {AiryBi}\left (\alpha \right ) \alpha d \alpha \right ) \operatorname {AiryAi}\left (x \right )-\frac {\operatorname {AiryBi}\left (x \right ) x^{3} \operatorname {hypergeom}\left (\left [1\right ], \left [\frac {4}{3}, 2\right ], \frac {x^{3}}{9}\right ) 3^{\frac {1}{6}} \Gamma \left (\frac {2}{3}\right )}{6}+\frac {\operatorname {AiryBi}\left (x \right ) \sqrt {x}\, \left (x^{\frac {3}{2}}\right )^{\frac {1}{3}} \pi \operatorname {BesselI}\left (\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -1 \]

Problem 7168

ODE	\[ \boxed {y^{\prime \prime }-y x=x^{2}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+\frac {\left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}} \operatorname {hypergeom}\left (\left [1\right ], \left [\frac {2}{3}, 2\right ], \frac {x^{3}}{9}\right ) x^{\frac {7}{2}}-3 \Gamma \left (\frac {2}{3}\right ) \left (3 \sqrt {x}\, \operatorname {AiryAi}\left (x \right ) \left (\int _{0}^{x}\operatorname {AiryBi}\left (\alpha \right ) \alpha ^{2}d \alpha \right )+\left (x^{\frac {3}{2}}\right )^{\frac {2}{3}} \operatorname {AiryBi}\left (x \right ) \left (\operatorname {BesselI}\left (-\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right ) x^{\frac {3}{2}}-\operatorname {BesselI}\left (\frac {1}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right )\right )\right )\right ) \pi }{9 \sqrt {x}\, \Gamma \left (\frac {2}{3}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -x \]

Problem 7169

ODE	\[ \boxed {y^{\prime \prime }-y x=x^{3}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\frac {x^{4} \left (-\frac {5 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right )}{6}+x \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right )\right )}{10 \Gamma \left (\frac {2}{3}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {5 x^{4} \pi \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right ) \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right )-6 \Gamma \left (\frac {2}{3}\right ) \left (x^{5} \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right ) \Gamma \left (\frac {2}{3}\right )-10 \operatorname {AiryBi}\left (x \right ) c_{1} -10 \operatorname {AiryAi}\left (x \right ) c_{2} \right )}{60 \Gamma \left (\frac {2}{3}\right )} \]

Problem 7170

ODE	\[ \boxed {y^{\prime \prime }-y x=x^{6}+x^{3}-42} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\frac {x \left (-\frac {16 x^{6} \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {7}{3}\right ], \left [\frac {2}{3}, \frac {10}{3}\right ], \frac {x^{3}}{9}\right )}{21}+x^{7} \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right ) \operatorname {hypergeom}\left (\left [\frac {8}{3}\right ], \left [\frac {4}{3}, \frac {11}{3}\right ], \frac {x^{3}}{9}\right )+224 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )+\frac {8 x \left (-105 \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right ) \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right )+x^{2} \left (-\frac {5 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right )}{6}+x \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \Gamma \left (\frac {2}{3}\right )^{2} \left (\operatorname {AiryAi}\left (x \right ) 3^{\frac {2}{3}}+\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{6}}\right )\right )\right )}{5}\right )}{16 \Gamma \left (\frac {2}{3}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -x^{5}-21 x^{2} \]

Problem 7171

ODE	\[ \boxed {y^{\prime \prime }-y x^{2}=x^{2}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\frac {\left (-1\right )^{\frac {1}{8}} \left (\frac {x \Gamma \left (\frac {3}{4}\right ) \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )\right ) \left (x^{2}\right )^{\frac {3}{4}} \operatorname {hypergeom}\left (\left [1\right ], \left [\frac {5}{4}, 2\right ], \frac {x^{4}}{16}\right )}{2}+\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right ) \left (-1\right )^{\frac {3}{4}} \operatorname {BesselI}\left (\frac {3}{4}, \frac {x^{2}}{2}\right ) \pi \sqrt {2}\right ) x^{\frac {7}{2}}}{4 \left (x^{2}\right )^{\frac {3}{4}}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} -1 \]

Problem 7172

ODE	\[ \boxed {y^{\prime \prime }-y x^{2}=x^{3}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\frac {\left (-1\right )^{\frac {1}{8}} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right ) \operatorname {hypergeom}\left (\left [1\right ], \left [\frac {3}{4}, 2\right ], \frac {x^{4}}{16}\right ) \left (-1\right )^{\frac {3}{4}} \left (x^{2}\right )^{\frac {1}{4}} x^{3}+2 \Gamma \left (\frac {3}{4}\right ) \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )\right ) \left (\operatorname {BesselI}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) x^{2}-\operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )\right )\right ) \pi \,x^{\frac {3}{2}}}{8 \left (x^{2}\right )^{\frac {1}{4}} \Gamma \left (\frac {3}{4}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} -x \]

Problem 7173

ODE	\[ \boxed {y^{\prime \prime }-y x^{2}=x^{4}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\frac {\left (-1\right )^{\frac {1}{8}} \left (\frac {5 x \Gamma \left (\frac {3}{4}\right )^{2} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}\right ], \left [\frac {5}{4}, \frac {5}{2}\right ], \frac {x^{4}}{16}\right )}{6}+\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right ) \left (-1\right )^{\frac {3}{4}} \operatorname {hypergeom}\left (\left [\frac {5}{4}\right ], \left [\frac {3}{4}, \frac {9}{4}\right ], \frac {x^{4}}{16}\right ) \pi \right ) x^{\frac {11}{2}}}{10 \Gamma \left (\frac {3}{4}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (-\frac {6 x^{5} \pi ^{2} \operatorname {csgn}\left (x \right ) \operatorname {hypergeom}\left (\left [\frac {5}{4}\right ], \left [\frac {3}{4}, \frac {5}{2}\right ], \frac {x^{4}}{16}\right ) \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )}{5}+\Gamma \left (\frac {3}{4}\right ) \left (2 x^{6} \Gamma \left (\frac {3}{4}\right ) \operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}\right ], \left [\frac {5}{4}, \frac {5}{2}\right ], \frac {x^{4}}{16}\right )+\pi \left (x^{6} \Gamma \left (\frac {3}{4}\right ) \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}\right ], \left [\frac {19}{8}, \frac {5}{2}\right ], \frac {x^{4}}{16}\right ) \sqrt {2}-12 \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} -12 \operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} \right )\right )\right ) \sqrt {x}}{12 \pi \Gamma \left (\frac {3}{4}\right )} \]

Problem 7174

ODE	\[ \boxed {y^{\prime \prime }-y x^{2}=x^{4}-2} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\frac {\left (-5 x \Gamma \left (\frac {3}{4}\right )^{2} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{16}\right )+\frac {5 \Gamma \left (\frac {3}{4}\right )^{2} x^{5} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}\right ], \left [\frac {5}{4}, \frac {5}{2}\right ], \frac {x^{4}}{16}\right )}{6}+\left (-1\right )^{\frac {3}{4}} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i x^{2}}{2}\right ) \left (\operatorname {hypergeom}\left (\left [\frac {5}{4}\right ], \left [\frac {3}{4}, \frac {9}{4}\right ], \frac {x^{4}}{16}\right ) x^{4}-10 \operatorname {hypergeom}\left (\left [\frac {1}{4}\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{16}\right )\right ) \pi \right ) \left (-1\right )^{\frac {1}{8}} x^{\frac {3}{2}}}{10 \Gamma \left (\frac {3}{4}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} -x^{2} \]

Problem 7175

ODE	\[ \boxed {y^{\prime \prime }-2 y x^{2}=x^{4}-1} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )-\frac {\left (-1\right )^{\frac {1}{8}} x^{\frac {3}{2}} \left (-5 x \Gamma \left (\frac {3}{4}\right )^{2} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{8}\right )+\frac {5 \Gamma \left (\frac {3}{4}\right )^{2} x^{5} \left (\operatorname {BesselJ}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )-\operatorname {BesselY}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}\right ], \left [\frac {5}{4}, \frac {5}{2}\right ], \frac {x^{4}}{8}\right )}{3}+2^{\frac {3}{4}} \left (-1\right )^{\frac {3}{4}} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {i \sqrt {2}\, x^{2}}{2}\right ) \left (\operatorname {hypergeom}\left (\left [\frac {5}{4}\right ], \left [\frac {3}{4}, \frac {9}{4}\right ], \frac {x^{4}}{8}\right ) x^{4}-5 \operatorname {hypergeom}\left (\left [\frac {1}{4}\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{8}\right )\right ) \pi \right ) 2^{\frac {1}{8}}}{20 \Gamma \left (\frac {3}{4}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{4}, \frac {\sqrt {2}\, x^{2}}{2}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{4}, \frac {\sqrt {2}\, x^{2}}{2}\right ) c_{1} -\frac {x^{2}}{2} \]

Problem 7176

ODE	\[ \boxed {y^{\prime \prime }-x^{3} y=x^{3}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )+\frac {\sqrt {x}\, \left (5^{\frac {4}{5}} \left (-1\right )^{\frac {1}{10}} \sin \left (\frac {\pi }{5}\right ) \Gamma \left (\frac {4}{5}\right ) x^{5} \operatorname {hypergeom}\left (\left [1\right ], \left [\frac {6}{5}, 2\right ], \frac {x^{5}}{25}\right ) \operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )-5 \pi \left (\int _{0}^{x}\alpha ^{\frac {7}{2}} \operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i \alpha ^{\frac {5}{2}}}{5}\right )d \alpha \right ) \operatorname {BesselJ}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )\right )}{25} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{1} -1 \]

Problem 7177

ODE	\[ \boxed {y^{\prime \prime }-x^{3} y=x^{4}} \]
program solution	\[ y = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )-\frac {\left (\left (\int _{0}^{x}\alpha ^{\frac {9}{2}} \operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i \alpha ^{\frac {5}{2}}}{5}\right )d \alpha \right ) \operatorname {BesselJ}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right ) \left (x^{\frac {5}{2}}\right )^{\frac {1}{5}}+\operatorname {BesselY}\left (\frac {1}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right ) \left (-1\right )^{\frac {1}{10}} \left (x \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right )-\operatorname {BesselI}\left (-\frac {4}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) x^{\frac {7}{2}}\right )\right ) \sqrt {x}\, \pi }{5 \left (x^{\frac {5}{2}}\right )^{\frac {1}{5}}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{1} -x \]

Problem 7178

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

Problem 7179

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime } x^{3}-x^{3} y=x^{3}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7180

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

Problem 7181

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

Problem 7182

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

Problem 7183

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

Problem 7184

ODE	\[ \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x}-y x=x^{2}+\frac {1}{x}} \]
program solution	\[ y = c_{1} x \operatorname {BesselJ}\left (\frac {2}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )+c_{2} x \operatorname {BesselY}\left (\frac {2}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\frac {x \pi \left (\left (\int _{0}^{x}\frac {\operatorname {BesselY}\left (\frac {2}{3}, \frac {2 i \alpha ^{\frac {3}{2}}}{3}\right ) \left (\alpha ^{3}+1\right )}{\alpha }d \alpha \right ) \operatorname {BesselJ}\left (\frac {2}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )-\left (\int _{0}^{x}\frac {\operatorname {BesselJ}\left (\frac {2}{3}, \frac {2 i \alpha ^{\frac {3}{2}}}{3}\right ) \left (\alpha ^{3}+1\right )}{\alpha }d \alpha \right ) \operatorname {BesselY}\left (\frac {2}{3}, \frac {2 i x^{\frac {3}{2}}}{3}\right )\right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (-1+\operatorname {BesselI}\left (\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right ) c_{2} +\operatorname {BesselK}\left (\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right ) c_{1} \right ) \]

Problem 7185

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

Problem 7186

ODE	\[ \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y=x^{4}+\frac {1}{x}} \]
program solution	\[ y = c_{1} x \operatorname {BesselJ}\left (\frac {2}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )+c_{2} x \operatorname {BesselY}\left (\frac {2}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )-\frac {x \pi \left (\left (\int _{0}^{x}\frac {\operatorname {BesselY}\left (\frac {2}{5}, \frac {2 i \alpha ^{\frac {5}{2}}}{5}\right ) \left (\alpha ^{5}+1\right )}{\alpha }d \alpha \right ) \operatorname {BesselJ}\left (\frac {2}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )-\left (\int _{0}^{x}\frac {\operatorname {BesselJ}\left (\frac {2}{5}, \frac {2 i \alpha ^{\frac {5}{2}}}{5}\right ) \left (\alpha ^{5}+1\right )}{\alpha }d \alpha \right ) \operatorname {BesselY}\left (\frac {2}{5}, \frac {2 i x^{\frac {5}{2}}}{5}\right )\right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (-1+\operatorname {BesselI}\left (\frac {2}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{2} +\operatorname {BesselK}\left (\frac {2}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{1} \right ) \]

Problem 7187

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime } x^{3}-y x=x^{3}+x^{2}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7188

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

Problem 7189

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime } x^{3}-x^{3} y=x^{4}+x^{3}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7190

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime } x^{3}-y x^{2}=x^{3}} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {x}{2}+c_{1} \operatorname {hypergeom}\left (\left [\frac {1}{5}\right ], \left [\frac {3}{5}, \frac {4}{5}\right ], \frac {x^{5}}{25}\right )+c_{2} x \operatorname {hypergeom}\left (\left [\frac {2}{5}\right ], \left [\frac {4}{5}, \frac {6}{5}\right ], \frac {x^{5}}{25}\right )+c_{3} x^{2} \operatorname {hypergeom}\left (\left [\frac {3}{5}\right ], \left [\frac {6}{5}, \frac {7}{5}\right ], \frac {x^{5}}{25}\right ) \]

Problem 7191

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

Problem 7192

ODE	\[ \boxed {w^{\prime }+\frac {\sqrt {1-12 w}}{2}=-{\frac {1}{2}}} \] With initial conditions \begin {align*} [w \left (1\right ) = -1] \end {align*}
program solution	\[ \frac {\sqrt {1-12 w}}{3}-\frac {\ln \left (1+\sqrt {1-12 w}\right )}{3} = z -1+\frac {\sqrt {13}}{3}-\frac {\ln \left (1+\sqrt {13}\right )}{3} \] Verified OK.
Maple solution	\[ w \left (z \right ) = \operatorname {RootOf}\left (-i \pi +2 \sqrt {13}-2 \sqrt {1-12 \textit {\_Z}}+\ln \left (\textit {\_Z} \right )-\ln \left (-1+\sqrt {1-12 \textit {\_Z}}\right )+\ln \left (1+\sqrt {1-12 \textit {\_Z}}\right )-\ln \left (1+\sqrt {13}\right )+\ln \left (-1+\sqrt {13}\right )+6 z -6\right ) \]

Problem 7193

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

Problem 7194

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

Problem 7195

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (0\right ) = 1, y \left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {3 \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {3 \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \]

Problem 7196

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

Problem 7197

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

Problem 7198

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (0\right ) = 0] \end {align*}
program solution	\[ y = -\frac {\sin \left (x \right ) \tan \left (1\right )}{2}+\frac {\sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-\tan \left (1\right )+1\right ) \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \]

Problem 7199

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (2\right ) = 0] \end {align*}
program solution	\[ y = \frac {\left (-x +\cos \left (2\right )-\sin \left (2\right )+1\right ) \cos \left (x \right )}{2}+\frac {\left (\sin \left (2\right )-\tan \left (1\right )+\cos \left (2\right )\right ) \sin \left (x \right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-x +\cos \left (2\right )-\sin \left (2\right )+1\right ) \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) \left (\sin \left (2\right )-\tan \left (1\right )+\cos \left (2\right )\right )}{2} \]

Problem 7200

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 0, y \left (0\right ) = 0] \end {align*}
program solution	\[ y = -\frac {\sin \left (x \right ) \tan \left (1\right )}{2}+\frac {\sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-\tan \left (1\right )+1\right ) \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \]