2.17.123 Problems 12201 to 12300

Problem 12201

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

Problem 12202

ODE
program solution
Maple solution	\begin{align*} y \left (x \right ) &= c_{1} x +c_{2} \\ y \left (x \right ) &= \frac {\left (c_{2} +x \right )^{8} c_{1}}{2612736}+c_{3} x +c_{4} \\ \end{align*}

Problem 12203

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

Problem 12204

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (3 x \right ) \cos \left (x \right )} \]
program solution	\[ y = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )-\frac {\sin \left (2 x \right )}{6}-\frac {\sin \left (4 x \right )}{30} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )-\frac {\sin \left (2 x \right )}{6}-\frac {\sin \left (4 x \right )}{30} \]

Problem 12205

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

Problem 12206

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

Problem 12207

ODE	\begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) \end {align*} With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 1] \]
program solution
Maple solution	\begin{align*} x \left (t \right ) &= \sin \left (t \right ) \\ y \left (t \right ) &= \cos \left (t \right ) \\ \end{align*}

Problem 12208

ODE	\begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{2 t} \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{\left (\sqrt {15}-1\right ) t} c_{2} +{\mathrm e}^{-\left (1+\sqrt {15}\right ) t} c_{1} +\frac {{\mathrm e}^{2 t}}{6}+\frac {2 \,{\mathrm e}^{t}}{11} \\ y \left (t \right ) &= -{\mathrm e}^{\left (\sqrt {15}-1\right ) t} c_{2} \sqrt {15}+{\mathrm e}^{-\left (1+\sqrt {15}\right ) t} c_{1} \sqrt {15}-4 \,{\mathrm e}^{\left (\sqrt {15}-1\right ) t} c_{2} -4 \,{\mathrm e}^{-\left (1+\sqrt {15}\right ) t} c_{1} -\frac {{\mathrm e}^{t}}{11}-\frac {7 \,{\mathrm e}^{2 t}}{6} \\ \end{align*}

Problem 12209

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

Problem 12210

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

Problem 12211

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

Problem 12212

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

Problem 12213

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

Problem 12214

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

Problem 12215

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

Problem 12216

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

Problem 12217

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

Problem 12218

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

Problem 12219

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

Problem 12220

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

Problem 12221

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

Problem 12222

ODE	\[ \boxed {y^{\prime \prime \prime }+y x=\sin \left (x \right )} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 12223

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

Problem 12224

ODE	\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }=2 x^{2}+3} \]
program solution	\[ y = c_{1} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x} c_{2} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x} c_{3} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x} c_{4} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x} c_{5} +\frac {2 x^{3}}{3}+3 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )^{2} \left (\frac {3 c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\left (\frac {3 c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) \left (\frac {3 c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\left (\frac {3 c_{4} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) \left (x^{3}+\frac {9}{2} x +\frac {3}{2} c_{5} \right )\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )\right )\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )-1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )^{2} \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )-1\right )}{3} \]

Problem 12225

ODE
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12226

ODE	\[ \boxed {y^{\prime \prime \prime }+y x=\cosh \left (x \right )} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 12227

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

Problem 12228

ODE	\[ \boxed {y^{\prime \prime \prime }+y x=\cosh \left (x \right )} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 12229

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

Problem 12230

ODE	\[ \boxed {\sinh \left (x \right ) {y^{\prime }}^{2}+3 y=0} \]
program solution	\[ y = \frac {\left (\int \sqrt {-\frac {3}{\sinh \left (x \right )}}d x \right )^{2}}{4}+\frac {\left (\int \sqrt {-\frac {3}{\sinh \left (x \right )}}d x \right ) c_{1}}{2}+\frac {c_{1}^{2}}{4} \] Verified OK. \[ y = \frac {\left (\int \sqrt {-\frac {3}{\sinh \left (x \right )}}d x \right )^{2}}{4}+\frac {\left (\int \sqrt {-\frac {3}{\sinh \left (x \right )}}d x \right ) c_{1}}{2}+\frac {c_{1}^{2}}{4} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (-\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \sqrt {-{\mathrm e}^{x}+1}\, \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \left (\sqrt {3}\, \sqrt {2}\, \sqrt {-{\mathrm e}^{x} \left ({\mathrm e}^{2 x}-1\right )}\, c_{1} -2 \textit {\_Z} \right ) {\mathrm e}^{-x}}{12 \,{\mathrm e}^{2 x}-12}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \sqrt {-{\mathrm e}^{x}+1}\, \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \left (\sqrt {3}\, \sqrt {2}\, \sqrt {-{\mathrm e}^{x} \left ({\mathrm e}^{2 x}-1\right )}\, c_{1} +2 \textit {\_Z} \right ) {\mathrm e}^{-x}}{12 \,{\mathrm e}^{2 x}-12}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \left (3 \,{\mathrm e}^{2 x} \operatorname {RootOf}\left (-1+\left (-6 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}\right ) \textit {\_Z}^{2}\right ) c_{1} -\textit {\_Z} \,{\mathrm e}^{-x}-3 c_{1} \operatorname {RootOf}\left (-1+\left (-6 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}\right ) \textit {\_Z}^{2}\right )\right )}{6 \sqrt {-{\mathrm e}^{x}+1}\, \left ({\mathrm e}^{x}+1\right )}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \sqrt {-{\mathrm e}^{x}+1}\, \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \left (\sqrt {3}\, \sqrt {2}\, \sqrt {-{\mathrm e}^{x} \left ({\mathrm e}^{2 x}-1\right )}\, c_{1} -2 \textit {\_Z} \right ) {\mathrm e}^{-x}}{12 \,{\mathrm e}^{2 x}-12}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (-\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \sqrt {-{\mathrm e}^{x}+1}\, \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \left (\sqrt {3}\, \sqrt {2}\, \sqrt {-{\mathrm e}^{x} \left ({\mathrm e}^{2 x}-1\right )}\, c_{1} +2 \textit {\_Z} \right ) {\mathrm e}^{-x}}{12 \,{\mathrm e}^{2 x}-12}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ y \left (x \right ) &= -\frac {{\operatorname {RootOf}\left (-\operatorname {JacobiSN}\left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-2 \,{\mathrm e}^{x}-2, \operatorname {index} &=1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{x}, \operatorname {index} &=1\right ) \left (3 \,{\mathrm e}^{2 x} \operatorname {RootOf}\left (-1+\left (-6 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}\right ) \textit {\_Z}^{2}\right ) c_{1} -\textit {\_Z} \,{\mathrm e}^{-x}-3 c_{1} \operatorname {RootOf}\left (-1+\left (-6 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}\right ) \textit {\_Z}^{2}\right )\right )}{6 \sqrt {-{\mathrm e}^{x}+1}\, \left ({\mathrm e}^{x}+1\right )}, \frac {\sqrt {2}}{2}\right )+\sqrt {-{\mathrm e}^{x}+1}\right )}^{2} {\mathrm e}^{-x}}{6 \,{\mathrm e}^{2 x}-6} \\ \end{align*}

Problem 12231

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

Problem 12232

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

Problem 12233

ODE	\[ \boxed {2 y^{\prime \prime }+3 y^{\prime }+4 y x^{2}=1} \]
program solution
Maple solution	\[ y \left (x \right ) = -48 \left (-\frac {32 \operatorname {KummerM}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \left (i+\frac {3 \sqrt {2}}{32}\right ) \left (\int \frac {\operatorname {KummerU}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) {\mathrm e}^{\frac {i \sqrt {2}\, x^{2}}{2}+\frac {3 x}{4}}}{1563 i \operatorname {KummerU}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \operatorname {KummerM}\left (-\frac {9 i \sqrt {2}}{128}-\frac {1}{4}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right )+2048 \operatorname {KummerM}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \operatorname {KummerU}\left (-\frac {9 i \sqrt {2}}{128}-\frac {1}{4}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \left (i+\frac {3 \sqrt {2}}{32}\right )}d x \right )}{3}+\left (\int \frac {\operatorname {KummerM}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) {\mathrm e}^{\frac {i \sqrt {2}\, x^{2}}{2}+\frac {3 x}{4}}}{\left (192 i \sqrt {2}-2048\right ) \operatorname {KummerU}\left (-\frac {9 i \sqrt {2}}{128}-\frac {1}{4}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \operatorname {KummerM}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right )-1563 \operatorname {KummerU}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) \operatorname {KummerM}\left (-\frac {9 i \sqrt {2}}{128}-\frac {1}{4}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right )}d x \right ) \left (i \sqrt {2}-\frac {32}{3}\right ) \operatorname {KummerU}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right )-\frac {\operatorname {KummerU}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) c_{1}}{48}-\frac {\operatorname {KummerM}\left (\frac {3}{4}-\frac {9 i \sqrt {2}}{128}, \frac {3}{2}, i \sqrt {2}\, x^{2}\right ) c_{2}}{48}\right ) x \,{\mathrm e}^{-\frac {\left (i \sqrt {2}\, x +\frac {3}{2}\right ) x}{2}} \]

Problem 12234

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

Problem 12235

ODE	\[ \boxed {x^{2} y^{\prime \prime }-y=\sin \left (x \right )^{2}} \]
program solution	\[ y = c_{1} x^{\frac {1}{2}-\frac {\sqrt {5}}{2}}+\frac {c_{2} \sqrt {5}\, x^{\frac {1}{2}+\frac {\sqrt {5}}{2}}}{5}+\frac {x^{2} \left (\left (3+\sqrt {5}\right ) \operatorname {hypergeom}\left (\left [1, \frac {3}{4}-\frac {\sqrt {5}}{4}\right ], \left [\frac {3}{2}, 2, \frac {7}{4}-\frac {\sqrt {5}}{4}\right ], -x^{2}\right )+\operatorname {hypergeom}\left (\left [1, \frac {\sqrt {5}}{4}+\frac {3}{4}\right ], \left [\frac {3}{2}, 2, \frac {7}{4}+\frac {\sqrt {5}}{4}\right ], -x^{2}\right ) \left (\sqrt {5}-3\right )\right ) \sqrt {5}}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {3 \left (\sqrt {5}+\frac {5}{3}\right ) x^{2} \operatorname {hypergeom}\left (\left [1, -\frac {\sqrt {5}}{4}+\frac {3}{4}\right ], \left [\frac {3}{2}, 2, \frac {7}{4}-\frac {\sqrt {5}}{4}\right ], -x^{2}\right )}{10}-\frac {3 x^{2} \left (\sqrt {5}-\frac {5}{3}\right ) \operatorname {hypergeom}\left (\left [1, \frac {\sqrt {5}}{4}+\frac {3}{4}\right ], \left [\frac {3}{2}, 2, \frac {7}{4}+\frac {\sqrt {5}}{4}\right ], -x^{2}\right )}{10}+x^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} c_{1} +x^{\frac {\sqrt {5}}{2}+\frac {1}{2}} c_{2} \]

Problem 12236

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

Problem 12237

ODE
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12238

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

Problem 12239

ODE
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12240

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

Problem 12241

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 12242

ODE
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12243

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

Problem 12244

ODE	\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y=0} \]
program solution	\[ y = {\mathrm e}^{\left (-\frac {\left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}{6}-\frac {11}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}+\frac {5}{3}+\frac {i \sqrt {3}\, \left (\frac {\left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}{3}-\frac {22}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}\right )}{2}\right ) x} c_{1} +{\mathrm e}^{\left (\frac {\left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}{3}+\frac {22}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}+\frac {5}{3}\right ) x} c_{2} +{\mathrm e}^{\left (-\frac {\left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}{6}-\frac {11}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}+\frac {5}{3}-\frac {i \sqrt {3}\, \left (\frac {\left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}{3}-\frac {22}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}\right )}{2}\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\left (\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}+5 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}+22\right ) x}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}}-c_{2} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-10 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (116+6 \sqrt {3}\, \sqrt {26}\right )^{\frac {2}{3}}-22\right ) x}{6 \left (116+6 \sqrt {3}\, \sqrt {26}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-10 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (116+6 \sqrt {3}\, \sqrt {26}\right )^{\frac {2}{3}}-22\right ) x}{6 \left (116+6 \sqrt {3}\, \sqrt {26}\right )^{\frac {1}{3}}}\right ) \]

Problem 12245

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

Problem 12246

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

Problem 12247

ODE	\[ \boxed {\left (x -3\right ) y^{\prime \prime }+\ln \left (x \right ) y=x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 2] \end {align*}
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12248

ODE	\[ \boxed {y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right )=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 1, y^{\prime }\left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 12249

ODE	\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (x -1\right )+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution
Maple solution	\[ y \left (x \right ) = \frac {-20 \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right ) {\mathrm e}^{\left (\frac {1}{4}-\frac {i}{4}\right ) \pi } \left (x +i\right )^{\frac {1}{2}+\frac {i}{2}} \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )+20 \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )}{\left (10-10 i\right ) \left (\operatorname {hypergeom}\left (\left [1-i, 1+i\right ], \left [\frac {3}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )-\operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right )+\left (-1+7 i\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}+\frac {3 i}{2}, \frac {3}{2}-\frac {i}{2}\right ], \left [\frac {5}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )} \]

Problem 12250

ODE	\[ \boxed {x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right )=\sinh \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12251

ODE	\[ \boxed {\sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12252

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime } \left (x -1\right )+y x^{2}=\tan \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 12253

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

Problem 12254

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

Problem 12255

ODE	\[ \boxed {y^{\prime \prime }+\frac {k x}{y^{4}}=0} \]
program solution
Maple solution	\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (15 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-\textit {\_f}^{4} c_{1} +50 \textit {\_f} k}\, \textit {\_f}}{\textit {\_f}^{3} c_{1} -50 k}d \textit {\_f} \right ) x -5 c_{2} x -3\right ) x \\ y \left (x \right ) &= \operatorname {RootOf}\left (15 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-\textit {\_f}^{4} c_{1} +50 \textit {\_f} k}\, \textit {\_f}}{\textit {\_f}^{3} c_{1} -50 k}d \textit {\_f} \right ) x +5 c_{2} x +3\right ) x \\ \end{align*}

Problem 12256

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

Problem 12257

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

Problem 12258

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

Problem 12259

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

Problem 12260

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 12261

ODE	\[ \boxed {x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, {\mathrm e}^{-\frac {x}{2}} \left (x c_{1} \left (x +2\right ) \operatorname {BesselI}\left (\frac {i \sqrt {7}}{2}+1, \frac {x}{2}\right )-x c_{2} \left (x +2\right ) \operatorname {BesselK}\left (\frac {i \sqrt {7}}{2}+1, \frac {x}{2}\right )+\left (\operatorname {BesselI}\left (\frac {i \sqrt {7}}{2}, \frac {x}{2}\right ) c_{1} +\operatorname {BesselK}\left (\frac {i \sqrt {7}}{2}, \frac {x}{2}\right ) c_{2} \right ) \left (-2+i \left (x +2\right ) \sqrt {7}+x^{2}+3 x \right )\right ) \]

Problem 12262

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

Problem 12263

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

Problem 12264

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

Problem 12265

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

Problem 12266

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

Problem 12267

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

Problem 12268

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

Problem 12269

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

Problem 12270

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

Problem 12271

ODE	\[ \boxed {y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }=\cos \left (x \right )} \]
program solution	\[ \frac {y^{2}}{2}-c_{1} \ln \left (-\cot \left (x \right )+\csc \left (x \right )\right )-x -c_{2} = 0 \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {12}\, \sqrt {\left (-{\mathrm e}^{2 i x}+1\right )^{3} \left (-\frac {i}{3}+\frac {{\mathrm e}^{3 i x} \pi \left (\operatorname {csgn}\left (i {\mathrm e}^{-i x}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )^{2}\right )-1\right ) \operatorname {csgn}\left (i {\mathrm e}^{-i x} \left ({\mathrm e}^{i x}-1\right )^{2}\right )}{2}-\frac {{\mathrm e}^{3 i x} \pi \left (\operatorname {csgn}\left (i {\mathrm e}^{-i x}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )^{2}\right )+1\right ) \operatorname {csgn}\left (i {\mathrm e}^{-i x} \left ({\mathrm e}^{i x}+1\right )^{2}\right )}{2}+\frac {{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )^{2}\right )}{2}-\frac {{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )^{2}\right )}{2}+6 \left (1-{\mathrm e}^{6 i x}+3 \,{\mathrm e}^{4 i x}-3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cos \left (x \right ) \cot \left (x \right )^{4} \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )+\frac {21 \left (1-{\mathrm e}^{6 i x}+3 \,{\mathrm e}^{4 i x}-3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cot \left (x \right ) \csc \left (x \right )^{3} \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )}{4}+12 \left (-1+{\mathrm e}^{6 i x}-3 \,{\mathrm e}^{4 i x}+3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cot \left (x \right )^{3} \csc \left (x \right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )-{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )\right )+{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )\right )-2 i {\mathrm e}^{3 i x} \ln \left ({\mathrm e}^{i x}+1\right )+2 i {\mathrm e}^{3 i x} \ln \left ({\mathrm e}^{i x}-1\right )+{\mathrm e}^{2 i x} \left (i+18 \left (-c_{2} +\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )+18 c_{1} \right )+18 \left (\left (c_{2} -\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )-c_{1} \right ) {\mathrm e}^{4 i x}+6 \left (\left (-c_{2} +\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )+c_{1} \right ) {\mathrm e}^{6 i x}+6 \left (c_{2} -\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )-6 c_{1} \right )}}{-6+6 \,{\mathrm e}^{6 i x}-18 \,{\mathrm e}^{4 i x}+18 \,{\mathrm e}^{2 i x}} \\ y \left (x \right ) &= \frac {\sqrt {12}\, \sqrt {\left (-{\mathrm e}^{2 i x}+1\right )^{3} \left (-\frac {i}{3}+\frac {{\mathrm e}^{3 i x} \pi \left (\operatorname {csgn}\left (i {\mathrm e}^{-i x}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )^{2}\right )-1\right ) \operatorname {csgn}\left (i {\mathrm e}^{-i x} \left ({\mathrm e}^{i x}-1\right )^{2}\right )}{2}-\frac {{\mathrm e}^{3 i x} \pi \left (\operatorname {csgn}\left (i {\mathrm e}^{-i x}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )^{2}\right )+1\right ) \operatorname {csgn}\left (i {\mathrm e}^{-i x} \left ({\mathrm e}^{i x}+1\right )^{2}\right )}{2}+\frac {{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )^{2}\right )}{2}-\frac {{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )^{2}\right )}{2}+6 \left (1-{\mathrm e}^{6 i x}+3 \,{\mathrm e}^{4 i x}-3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cos \left (x \right ) \cot \left (x \right )^{4} \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )+\frac {21 \left (1-{\mathrm e}^{6 i x}+3 \,{\mathrm e}^{4 i x}-3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cot \left (x \right ) \csc \left (x \right )^{3} \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )}{4}+12 \left (-1+{\mathrm e}^{6 i x}-3 \,{\mathrm e}^{4 i x}+3 \,{\mathrm e}^{2 i x}\right ) \left (\int \cot \left (x \right )^{3} \csc \left (x \right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )d x \right )-{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}-1\right )\right )+{\mathrm e}^{3 i x} \pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{i x}+1\right )\right )-2 i {\mathrm e}^{3 i x} \ln \left ({\mathrm e}^{i x}+1\right )+2 i {\mathrm e}^{3 i x} \ln \left ({\mathrm e}^{i x}-1\right )+{\mathrm e}^{2 i x} \left (i+18 \left (-c_{2} +\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )+18 c_{1} \right )+18 \left (\left (c_{2} -\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )-c_{1} \right ) {\mathrm e}^{4 i x}+6 \left (\left (-c_{2} +\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )+c_{1} \right ) {\mathrm e}^{6 i x}+6 \left (c_{2} -\sin \left (x \right )\right ) \operatorname {arctanh}\left (\cos \left (x \right )\right )-6 c_{1} \right )}}{-6+6 \,{\mathrm e}^{6 i x}-18 \,{\mathrm e}^{4 i x}+18 \,{\mathrm e}^{2 i x}} \\ \end{align*}

Problem 12272

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

Problem 12273

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

Problem 12274

ODE	\[ \boxed {y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}=0} \]
program solution	\[ y = c_{3} {\mathrm e}^{\int \frac {8 x^{2} c_{1} \sqrt {2}\, {\mathrm e}^{x -\frac {1}{2}} \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {2 x -1}}{2}\right )+8 \,{\mathrm e}^{-x +\frac {1}{2}} \sqrt {2 x -1}\, {\mathrm e}^{x -\frac {1}{2}} c_{1} x^{2}-8 x c_{1} \sqrt {2}\, {\mathrm e}^{x -\frac {1}{2}} \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {2 x -1}}{2}\right )-8 \,{\mathrm e}^{x -\frac {1}{2}} c_{1} {\mathrm e}^{-x +\frac {1}{2}} \sqrt {2 x -1}\, x +2 c_{1} \sqrt {2}\, {\mathrm e}^{x -\frac {1}{2}} \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {2 x -1}}{2}\right )+48 c_{2} x^{2} {\mathrm e}^{x}+2 \,{\mathrm e}^{x -\frac {1}{2}} c_{1} {\mathrm e}^{-x +\frac {1}{2}} \sqrt {2 x -1}-8 \sqrt {2 x -1}\, c_{1} x^{2}-48 c_{2} x \,{\mathrm e}^{x}+16 \sqrt {2 x -1}\, c_{1} x +12 \,{\mathrm e}^{x} c_{2} -4 \sqrt {2 x -1}\, c_{1}}{\left (2 x -1\right )^{\frac {3}{2}} \left (2 x c_{1} \sqrt {2}\, {\mathrm e}^{x -\frac {1}{2}} \sqrt {\pi }\, \sqrt {2 x -1}\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {2 x -1}}{2}\right )-c_{1} \sqrt {2}\, {\mathrm e}^{x -\frac {1}{2}} \sqrt {\pi }\, \sqrt {2 x -1}\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {2 x -1}}{2}\right )+12 c_{2} \sqrt {2 x -1}\, x \,{\mathrm e}^{x}-6 c_{2} \sqrt {2 x -1}\, {\mathrm e}^{x}+4 c_{1} x -4 c_{1} \right )}d x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {2 \,2^{\frac {3}{4}} {\mathrm e}^{-\frac {1}{4}} \left (\frac {\left (\frac {2 \left (\operatorname {erf}\left (\frac {\sqrt {-2+4 x}}{2}\right )-1\right ) c_{2}}{3}+\operatorname {erf}\left (\frac {\sqrt {-2+4 x}}{2}\right ) c_{1} \right ) \sqrt {-2+4 x}\, \left (-\frac {1}{2}+x \right ) \sqrt {\pi }}{2}+\left (-1+x \right ) {\mathrm e}^{\frac {1}{2}-x} \left (c_{1} +\frac {2 c_{2}}{3}\right )\right )}{\sqrt {-2+4 x}} \]

Problem 12275

ODE	\[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }-\left (25-6 x \right ) y=0} \]
program solution	\[ y = c_{1} \left (x +2\right )^{7} {\mathrm e}^{-x}+\frac {c_{2} \left (88447 \left (x +2\right )^{7} x^{4} {\mathrm e}^{-x -2} \operatorname {expIntegral}_{1}\left (-x -2\right )-11970 \,{\mathrm e}^{-x} x^{4} \left (x +2\right )^{7} \operatorname {expIntegral}_{1}\left (-x \right )+76477 x^{10}+970261 x^{9}+5171184 x^{8}[phone] x^{7}[phone] x^{6}[phone] x^{5}+9184784 x^{4}+488880 x^{3}-131040 x^{2}+60480 x -40320\right )}{322560 x^{4}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {88447 x^{4} c_{2} {\mathrm e}^{-x -2} \left (x +2\right )^{7} \operatorname {expIntegral}_{1}\left (-x -2\right )-11970 x^{4} c_{2} {\mathrm e}^{-x} \left (x +2\right )^{7} \operatorname {expIntegral}_{1}\left (-x \right )+x^{4} c_{1} \left (x +2\right )^{7} {\mathrm e}^{-x}+76477 c_{2} x^{10}+970261 c_{2} x^{9}+5171184 c_{2} x^{8}[phone] c_{2} x^{7}[phone] c_{2} x^{6}[phone] c_{2} x^{5}+9184784 c_{2} x^{4}+488880 c_{2} x^{3}-131040 c_{2} x^{2}+60480 c_{2} x -40320 c_{2}}{x^{4}} \]

Problem 12276

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

Problem 12277

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

Problem 12278

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

Problem 12279

ODE	\[ \boxed {\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y=0} \]
program solution
Maple solution	\[ y \left (x \right ) = -{\mathrm e}^{-\left (\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{-2 \sin \left (x \right )+\cos \left (x \right )}d x \right )} \left (c_{2} \left (\int \frac {\csc \left (x \right ) {\mathrm e}^{\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{-2 \sin \left (x \right )+\cos \left (x \right )}d x}}{-2 \sin \left (x \right )+\cos \left (x \right )}d x \right )-c_{1} \right ) \]

Problem 12280

ODE	\[ \boxed {y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 12281

ODE	\[ \boxed {y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y={\mathrm e}^{-2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x \left (3+x \right )}-\frac {i c_{2} \sqrt {\pi }\, {\mathrm e}^{-\frac {1}{4}-x^{2}-3 x} \operatorname {erf}\left (i \left (x +\frac {1}{2}\right )\right )}{2}+\frac {\sqrt {\pi }\, \left (i \operatorname {erf}\left (i \left (x +\frac {1}{2}\right )\right )+\operatorname {erfi}\left (\frac {1}{2}\right )\right ) {\mathrm e}^{-\frac {1}{4}-x^{2}-3 x}}{4}+\frac {{\mathrm e}^{-2 x}}{2}-\frac {{\mathrm e}^{-x \left (3+x \right )}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\left (x +3\right ) x} c_{2} +{\mathrm e}^{-\left (x +3\right ) x} \operatorname {erf}\left (i \left (x +\frac {1}{2}\right )\right ) c_{1} +\frac {{\mathrm e}^{-2 x}}{2} \]

Problem 12282

ODE	\[ \boxed {y^{\prime \prime }+9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = 2 \cos \left (3 t \right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = 2 \cos \left (3 t \right ) \]

Problem 12283

ODE	\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{\frac {t}{2}} \left (\cos \left (t \right )+\sin \left (t \right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = 2 \,{\mathrm e}^{\frac {t}{2}} \left (\cos \left (t \right )+\sin \left (t \right )\right ) \]

Problem 12284

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

Problem 12285

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
program solution	\[ y = 3 \,{\mathrm e}^{2 t} \sin \left (t \right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = 3 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

Problem 12286

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ y = \left ({\mathrm e}^{5 t}+1\right ) {\mathrm e}^{-2 t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left ({\mathrm e}^{5 t}+1\right ) {\mathrm e}^{-2 t} \]

Problem 12287

ODE	\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+37 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -3] \end {align*}
program solution	\[ y = \frac {2 \,{\mathrm e}^{\frac {t}{2}} \left (3 \cos \left (3 t \right )-2 \sin \left (3 t \right )\right )}{3} \] Verified OK.
Maple solution	\[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{\frac {t}{2}} \left (3 \cos \left (3 t \right )-2 \sin \left (3 t \right )\right )}{3} \]

Problem 12288

ODE	\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
program solution	\[ y = 7 \,{\mathrm e}^{-t}-5 \,{\mathrm e}^{-2 t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = 7 \,{\mathrm e}^{-t}-5 \,{\mathrm e}^{-2 t} \]

Problem 12289

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
program solution	\[ y = {\mathrm e}^{-t} \cos \left (2 t \right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{-t} \cos \left (2 t \right ) \]

Problem 12290

ODE	\[ \boxed {4 y^{\prime \prime }-12 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{\frac {3 t}{2}} \cos \left (t \right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = 2 \,{\mathrm e}^{\frac {3 t}{2}} \cos \left (t \right ) \]

Problem 12291

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -6] \end {align*}
program solution	\[ y = \frac {{\mathrm e}^{-2 t} \left (3 \cos \left (3 t \right )-4 \sin \left (3 t \right )\right )}{3} \] Verified OK.
Maple solution	\[ y \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (3 \cos \left (3 t \right )-4 \sin \left (3 t \right )\right )}{3} \]

Problem 12292

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -3] \end {align*}
program solution	\[ y = {\mathrm e}^{-3 t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{-3 t} \]

Problem 12293

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

Problem 12294

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
program solution	\[ y = -\frac {{\mathrm e}^{t} \sin \left (2 t \right )}{2} \] Verified OK.
Maple solution	\[ y \left (t \right ) = -\frac {\sin \left (2 t \right ) {\mathrm e}^{t}}{2} \]

Problem 12295

ODE	\[ \boxed {y^{\prime \prime }-20 y^{\prime }+51 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -14] \end {align*}
program solution	\[ y = -2 \,{\mathrm e}^{10 t} \sinh \left (7 t \right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = -2 \,{\mathrm e}^{10 t} \sinh \left (7 t \right ) \]

Problem 12296

ODE	\[ \boxed {2 y^{\prime \prime }+3 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -1] \end {align*}
program solution	\[ y = 4 \,{\mathrm e}^{-\frac {t}{2}}-{\mathrm e}^{-t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = -{\mathrm e}^{-t}+4 \,{\mathrm e}^{-\frac {t}{2}} \]

Problem 12297

ODE	\[ \boxed {3 y^{\prime \prime }+8 y^{\prime }-3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4] \end {align*}
program solution	\[ y = 3 \,{\mathrm e}^{-\frac {4 t}{3}} \cosh \left (\frac {5 t}{3}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = 3 \,{\mathrm e}^{-\frac {4 t}{3}} \cosh \left (\frac {5 t}{3}\right ) \]

Problem 12298

ODE	\[ \boxed {2 y^{\prime \prime }+20 y^{\prime }+51 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -5] \end {align*}
program solution	\[ y = {\mathrm e}^{-5 t} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{-5 t} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]

Problem 12299

ODE	\[ \boxed {4 y^{\prime \prime }+40 y^{\prime }+101 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -5] \end {align*}
program solution	\[ y = {\mathrm e}^{-5 t} \cos \left (\frac {t}{2}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{-5 t} \cos \left (\frac {t}{2}\right ) \]

Problem 12300

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+34 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ y = {\mathrm e}^{-3 t} \left (3 \cos \left (5 t \right )+2 \sin \left (5 t \right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{-3 t} \left (3 \cos \left (5 t \right )+2 \sin \left (5 t \right )\right ) \]