2.17.33 Problems 3201 to 3300

Problem 3201

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

Problem 3202

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

Problem 3203

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

Problem 3204

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

Problem 3205

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

Problem 3206

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

Problem 3207

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

Problem 3208

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

Problem 3209

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

Problem 3210

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

Problem 3211

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

Problem 3212

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

Problem 3213

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

Problem 3214

ODE	\[ \boxed {3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y=0} \]
program solution	\[ y = \frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}} \] Verified OK. \[ y = -\frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}} \] Verified OK. \[ y = \frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (-x \left (6 \ln \left (x \right ) x^{2}-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{6 \ln \left (x \right ) x^{2}-3 x^{2}-4 c_{1}} \\ y \left (x \right ) &= -\frac {2^{\frac {2}{3}} {\left (-x \left (6 \ln \left (x \right ) x^{2}-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12 \ln \left (x \right ) x^{2}-6 x^{2}-8 c_{1}} \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (-x \left (6 \ln \left (x \right ) x^{2}-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12 \ln \left (x \right ) x^{2}-6 x^{2}-8 c_{1}} \\ \end{align*}

Problem 3215

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

Problem 3216

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

Problem 3217

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

Problem 3218

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

Problem 3219

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

Problem 3220

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

Problem 3221

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

Problem 3222

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

Problem 3223

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

Problem 3224

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

Problem 3225

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

Problem 3226

ODE	\[ \boxed {-y^{\prime } \sqrt {1+{y^{\prime }}^{2}}=-x} \]
program solution	\[ y = \int \frac {\sqrt {2 \sqrt {4 x^{2}+1}-2}}{2}d x +c_{1} \] Verified OK. \[ y = \int -\frac {\sqrt {2 \sqrt {4 x^{2}+1}-2}}{2}d x +c_{2} \] Verified OK. \[ y = -\frac {i \sqrt {2}\, \left (-\frac {256 \sqrt {\pi }\, \sqrt {2}\, x^{3} \cosh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3}-\frac {8 \sqrt {\pi }\, \sqrt {2}\, \left (-\frac {64}{3} x^{4}-\frac {8}{3} x^{2}+\frac {2}{3}\right ) \sinh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{\sqrt {4 x^{2}+1}}\right )}{32 \sqrt {\pi }}+c_{3} \] Verified OK. \[ y = \frac {i \sqrt {2}\, \left (-\frac {256 \sqrt {\pi }\, \sqrt {2}\, x^{3} \cosh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3}-\frac {8 \sqrt {\pi }\, \sqrt {2}\, \left (-\frac {64}{3} x^{4}-\frac {8}{3} x^{2}+\frac {2}{3}\right ) \sinh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{\sqrt {4 x^{2}+1}}\right )}{32 \sqrt {\pi }}+c_{4} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {i \left (-32 x^{4}-4 x^{2}+1\right ) \sinh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3 \sqrt {4 x^{2}+1}}-\frac {16 i x^{3} \cosh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3}+c_{1} \\ y \left (x \right ) &= \frac {i \left (-32 x^{4}-4 x^{2}+1\right ) \sinh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3 \sqrt {4 x^{2}+1}}+\frac {16 i x^{3} \cosh \left (\frac {3 \,\operatorname {arcsinh}\left (2 x \right )}{2}\right )}{3}+c_{1} \\ y \left (x \right ) &= -\frac {\left (\int \sqrt {2 \sqrt {4 x^{2}+1}-2}d x \right )}{2}+c_{1} \\ y \left (x \right ) &= \frac {\left (\int \sqrt {2 \sqrt {4 x^{2}+1}-2}d x \right )}{2}+c_{1} \\ \end{align*}

Problem 3227

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

Problem 3228

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

Problem 3229

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

Problem 3230

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

Problem 3231

ODE	\[ \boxed {y-y^{\prime } x +x^{2} {y^{\prime }}^{3}=0} \]
program solution	\[ \frac {\ln \left (x \right )}{2}-\frac {\left (\int _{}^{\frac {y}{\sqrt {x}}}\frac {8+2^{\frac {1}{3}} \left (\textit {\_a} \sqrt {3}\, \sqrt {27 \textit {\_a}^{2}-4}+9 \textit {\_a}^{2}-4\right ) {\left (\left (3 \sqrt {3}\, \textit {\_a} -\sqrt {27 \textit {\_a}^{2}-4}\right )^{2}\right )}^{\frac {1}{3}}+2 \left (2 \sqrt {3}\, \textit {\_a} +\sqrt {27 \textit {\_a}^{2}-4}\right ) \left (-12 \sqrt {3}\, \textit {\_a} +4 \sqrt {27 \textit {\_a}^{2}-4}\right )^{\frac {1}{3}}-6 \textit {\_a}^{2}}{\textit {\_a} \left (\textit {\_a}^{2}+4\right )}d \textit {\_a} \right )}{6}-c_{1} = 0 \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -x^{2} \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}+8 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +4 c_{1} \right )^{3}+x \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}+8 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +4 c_{1} \right ) \\ y \left (x \right ) &= -x^{2} \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}-16 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +16 c_{1} \right )^{3}+x \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}-16 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +16 c_{1} \right ) \\ \end{align*}

Problem 3232

ODE	\[ \boxed {y \left (y-2 y^{\prime } x \right )^{3}-{y^{\prime }}^{2}=0} \]
program solution	\[ -\ln \left (x \right ) = \int _{}^{y x}-\frac {24 \textit {\_a} \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}}{36 \textit {\_a}^{2} \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}-24 \textit {\_a}^{2}+\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {3}}{9 x} \\ y \left (x \right ) &= \frac {\sqrt {3}}{9 x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +24 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{36 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}+\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}-\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} -48 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}-72 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}+\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}+2 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +48 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}+72 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}-\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}+24 \textit {\_a}^{2}-2 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}-1}d \textit {\_a} \right )\right )}{x} \\ \end{align*}

Problem 3233

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

Problem 3234

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

Problem 3235

ODE	\[ \boxed {x y^{2} \left (y^{\prime } x +y\right )=1} \]
program solution	\[ \frac {y^{3} x^{3}}{3}-\frac {x^{2}}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}

Problem 3236

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

Problem 3237

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

Problem 3238

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

Problem 3239

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

Problem 3240

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

Problem 3241

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

Problem 3242

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

Problem 3243

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

Problem 3244

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

Problem 3245

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

Problem 3246

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

Problem 3247

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

Problem 3248

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y=0} \]
program solution	\[ y = {\mathrm e}^{-3 i x} c_{1} +x \,{\mathrm e}^{-3 i x} c_{2} +{\mathrm e}^{3 i x} c_{3} +x \,{\mathrm e}^{3 i x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{4} x +c_{2} \right ) \cos \left (3 x \right )+\sin \left (3 x \right ) \left (c_{3} x +c_{1} \right ) \]

Problem 3249

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y=0} \]
program solution	\[ y = {\mathrm e}^{\left (-i+\sqrt {3}\right ) x} c_{1} +{\mathrm e}^{x \left (i-\sqrt {3}\right )} c_{2} +{\mathrm e}^{\left (-i-\sqrt {3}\right ) x} c_{3} +{\mathrm e}^{x \left (\sqrt {3}+i\right )} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -c_{1} {\mathrm e}^{\sqrt {3}\, x} \sin \left (x \right )+c_{2} {\mathrm e}^{-\sqrt {3}\, x} \sin \left (x \right )+c_{3} {\mathrm e}^{\sqrt {3}\, x} \cos \left (x \right )+c_{4} {\mathrm e}^{-\sqrt {3}\, x} \cos \left (x \right ) \]

Problem 3250

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

Problem 3251

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{3 x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{x} \]

Problem 3252

ODE	\[ \boxed {y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }=0} \]
program solution	\[ y = c_{3} x^{2}+c_{2} x +c_{1} +{\mathrm e}^{3 x} c_{4} +x \,{\mathrm e}^{3 x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{5} x +c_{4} \right ) {\mathrm e}^{3 x}+c_{3} x^{2}+c_{2} x +c_{1} \]

Problem 3253

ODE	\[ \boxed {y^{\left (6\right )}-64 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-\sqrt {2 i \sqrt {3}-2}\, x} c_{3} +{\mathrm e}^{\sqrt {-2 i \sqrt {3}-2}\, x} c_{4} +{\mathrm e}^{-\sqrt {-2 i \sqrt {3}-2}\, x} c_{5} +{\mathrm e}^{\sqrt {2 i \sqrt {3}-2}\, x} c_{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\left (c_{4} {\mathrm e}^{3 x}+c_{6} {\mathrm e}^{x}\right ) \cos \left (\sqrt {3}\, x \right )+\left (c_{3} {\mathrm e}^{3 x}+c_{5} {\mathrm e}^{x}\right ) \sin \left (\sqrt {3}\, x \right )+{\mathrm e}^{4 x} c_{1} +c_{2} \right ) \]

Problem 3254

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+10 y=3 x \,{\mathrm e}^{-3 x}-2 \cos \left (x \right ) {\mathrm e}^{3 x}} \]
program solution	\[ y = {\mathrm e}^{-3 x} \left (c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )\right )+3 x \,{\mathrm e}^{-3 x}-\frac {\cos \left (x \right ) {\mathrm e}^{3 x}}{20}-\frac {{\mathrm e}^{3 x} \sin \left (x \right )}{60} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} +3 x \right ) {\mathrm e}^{-3 x}-\frac {{\mathrm e}^{3 x} \left (\cos \left (x \right )+\frac {\sin \left (x \right )}{3}\right )}{20} \]

Problem 3255

ODE	\[ \boxed {y^{\prime \prime }-8 y^{\prime }+17 y={\mathrm e}^{4 x} \left (x^{2}-3 \sin \left (x \right ) x \right )} \]
program solution	\[ y = {\mathrm e}^{4 x} \left (c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )\right )+x^{2} {\mathrm e}^{4 x}-2 \,{\mathrm e}^{4 x}+\frac {3 x^{2} \cos \left (x \right ) {\mathrm e}^{4 x}}{4}-\frac {3 \,{\mathrm e}^{4 x} \sin \left (x \right ) x}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (3 x^{2}+4 c_{1} \right ) \cos \left (x \right )+\left (-3 x +4 c_{2} \right ) \sin \left (x \right )+4 x^{2}-8\right ) {\mathrm e}^{4 x}}{4} \]

Problem 3256

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=\left (x +{\mathrm e}^{x}\right ) \sin \left (x \right )} \]
program solution	\[ y = {\mathrm e}^{x} \left (c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )\right )-\frac {{\mathrm e}^{x} x \cos \left (x \right )}{2}+\frac {2 \cos \left (x \right ) x}{5}+\frac {\sin \left (x \right ) x}{5}+\frac {14 \cos \left (x \right )}{25}+\frac {2 \sin \left (x \right )}{25} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-25 x +50 c_{1} \right ) {\mathrm e}^{x}+20 x +28\right ) \cos \left (x \right )}{50}+\frac {\left (5 c_{2} {\mathrm e}^{x}+x +\frac {2}{5}\right ) \sin \left (x \right )}{5} \]

Problem 3257

ODE	\[ \boxed {y^{\prime \prime }+4 y=\sinh \left (x \right ) \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} \cos \left (2 x \right )+\frac {c_{2} \sin \left (2 x \right )}{2}+\frac {\left (-4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\frac {\sin \left (2 x \right ) \left ({\mathrm e}^{x}-{\mathrm e}^{-x}\right )}{34} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (34 c_{1} -4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\left (c_{2} +\frac {{\mathrm e}^{x}}{34}-\frac {{\mathrm e}^{-x}}{34}\right ) \sin \left (2 x \right ) \]

Problem 3258

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

Problem 3259

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

Problem 3260

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y={\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2}} \]
program solution	\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{2 i x}+{\mathrm e}^{-2 i x} c_{3} -\frac {{\mathrm e}^{2 x} \cos \left (2 x \right )}{40}-\frac {{\mathrm e}^{2 x} \sin \left (2 x \right )}{20}-\frac {x}{4}-\frac {x^{2}}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (80 c_{2} -2 \cos \left (2 x \right )-4 \sin \left (2 x \right )-5\right ) {\mathrm e}^{2 x}}{80}+\frac {\left (80 c_{1} -5\right ) \cos \left (2 x \right )}{80}+\frac {\left (80 c_{3} +5\right ) \sin \left (2 x \right )}{80}-\frac {x^{2}}{4}-\frac {x}{4} \]

Problem 3261

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }=x^{2}+x \,{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} +c_{2} {\mathrm e}^{x}+{\mathrm e}^{3 x} c_{3} -\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}+\frac {26 x}{27}+\frac {4 x^{2}}{9}+\frac {x^{3}}{9} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (1-2 x \right ) {\mathrm e}^{2 x}}{4}+\frac {x^{3}}{9}+\frac {4 x^{2}}{9}+\frac {c_{1} {\mathrm e}^{3 x}}{3}+c_{2} {\mathrm e}^{x}+\frac {26 x}{27}+c_{3} \]

Problem 3262

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }=7 x -3 \cos \left (x \right )} \]
program solution	\[ y = c_{2} x +c_{1} +{\mathrm e}^{i \sqrt {2}\, x} c_{3} +{\mathrm e}^{-i \sqrt {2}\, x} c_{4} +\frac {7 x^{3}}{12}+3 \cos \left (x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {7 x^{3}}{12}-\frac {\cos \left (\sqrt {2}\, x \right ) c_{1}}{2}-\frac {c_{2} \sin \left (\sqrt {2}\, x \right )}{2}+3 \cos \left (x \right )+c_{3} x +c_{4} \]

Problem 3263

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y=\sin \left (x \right ) \cos \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 i x}+c_{2} {\mathrm e}^{-2 i x}+{\mathrm e}^{i x} c_{3} +{\mathrm e}^{-i x} c_{4} -\frac {\left (\int \cos \left (2 x \right ) \sin \left (x \right )^{2}d x \right ) \cos \left (x \right )}{3}+\frac {2 \left (\cos \left (x \right )^{2}+\frac {5 \left (\int \sin \left (4 x \right )d x \right )}{8}+\frac {1}{6}\right ) \sin \left (x \right )}{15} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (40 c_{3} +\sin \left (x \right )\right ) \cos \left (x \right )^{2}}{20}+\frac {\left (24 c_{4} \sin \left (x \right )+x +12 c_{1} \right ) \cos \left (x \right )}{12}+\frac {\left (360 c_{2} -7\right ) \sin \left (x \right )}{360}-c_{3} \]

Problem 3264

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

Problem 3265

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

Problem 3266

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

Problem 3267

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

Problem 3268

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

Problem 3269

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

Problem 3270

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

Problem 3271

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

Problem 3272

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

Problem 3273

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

Problem 3274

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

Problem 3275

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

Problem 3276

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

Problem 3277

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

Problem 3278

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

Problem 3279

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

Problem 3280

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

Problem 3281

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

Problem 3282

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

Problem 3283

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

Problem 3284

ODE	\[ \boxed {y^{\prime }+2 y \cot \left (2 x \right )=4 \csc \left (x \right ) x \sec \left (x \right )^{2}} \]
program solution	\[ \int _{}^{x}\left (4 y \cos \left (\textit {\_a} \right )^{2}-2 y-8 \textit {\_a} \sec \left (\textit {\_a} \right )\right )d \textit {\_a} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 16 \,\operatorname {csgn}\left (\csc \left (2 x \right )\right ) \left (\sqrt {-\frac {{\mathrm e}^{4 i x}}{\left ({\mathrm e}^{4 i x}-1\right )^{2}}}\, \left (i \operatorname {dilog}\left (1+i {\mathrm e}^{i x}\right )-i \operatorname {dilog}\left (1-i {\mathrm e}^{i x}\right )-x \ln \left (1+i {\mathrm e}^{i x}\right )+x \ln \left (1-i {\mathrm e}^{i x}\right )\right )+\frac {\csc \left (2 x \right ) c_{1}}{16}\right ) \]

Problem 3285

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

Problem 3286

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

Problem 3287

ODE	\[ \boxed {y^{\prime }-4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right )=0} \]
program solution	\[ y = \frac {\left (c_{1} \sin \left (\textit {\_a} \right )^{3} \left (1-{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}}+8 \sin \left (\textit {\_a} \right )^{2} \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} \left (\int _{}^{x}\textit {\_a} \,{\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right )-c_{1} \sin \left (\textit {\_a} \right ) \left (1-{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}}-4 \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} \left (\int _{}^{x}\textit {\_a} \,{\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right )\right ) \left (1-{\mathrm e}^{i x}\right )^{4 x}}{\left (1-{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} {\mathrm e}^{4 i \left (-\operatorname {polylog}\left (2, -{\mathrm e}^{i x}\right )+\operatorname {polylog}\left (2, {\mathrm e}^{i x}\right )\right )} \sin \left (\textit {\_a} \right )^{3} \left (1+{\mathrm e}^{i x}\right )^{4 x}-4 \sin \left (\textit {\_a} \right )^{2} \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} \left (\int _{}^{x}\textit {\_a} \,{\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right ) \left (1-{\mathrm e}^{i x}\right )^{4 x}+4 \sin \left (\textit {\_a} \right )^{2} \left (\int _{}^{x}\textit {\_a} \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} {\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right ) \left (1-{\mathrm e}^{i x}\right )^{4 x}-\left (1-{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} {\mathrm e}^{4 i \left (-\operatorname {polylog}\left (2, -{\mathrm e}^{i x}\right )+\operatorname {polylog}\left (2, {\mathrm e}^{i x}\right )\right )} \sin \left (\textit {\_a} \right ) \left (1+{\mathrm e}^{i x}\right )^{4 x}+4 \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} \left (\int _{}^{x}\textit {\_a} \,{\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right ) \left (1-{\mathrm e}^{i x}\right )^{4 x}-4 \left (\int _{}^{x}\textit {\_a} \left (1+{\mathrm e}^{i \textit {\_a}}\right )^{4 \textit {\_a}} {\mathrm e}^{-4 i \left (\operatorname {polylog}\left (2, -{\mathrm e}^{i \textit {\_a}}\right )-\operatorname {polylog}\left (2, {\mathrm e}^{i \textit {\_a}}\right )\right )}d \textit {\_a} \right ) \left (1-{\mathrm e}^{i x}\right )^{4 x}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -4 \,{\mathrm e}^{4 i \left (\operatorname {dilog}\left ({\mathrm e}^{i x}+1\right )-\operatorname {dilog}\left (1-{\mathrm e}^{i x}\right )\right )} \left (1-{\mathrm e}^{i x}\right )^{4 x} \left (\int \csc \left (x \right ) \left (\sec \left (x \right )^{2}-2\right ) x \left (1-{\mathrm e}^{i x}\right )^{-4 x} \left ({\mathrm e}^{i x}+1\right )^{4 x} {\mathrm e}^{-4 i \left (\operatorname {dilog}\left ({\mathrm e}^{i x}+1\right )-\operatorname {dilog}\left (1-{\mathrm e}^{i x}\right )\right )}d x -\frac {c_{1}}{4}\right ) \left ({\mathrm e}^{i x}+1\right )^{-4 x} \]

Problem 3288

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

Problem 3289

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

Problem 3290

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

Problem 3291

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

Problem 3292

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

Problem 3293

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

Problem 3294

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

Problem 3295

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

Problem 3296

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

Problem 3297

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

Problem 3298

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

Problem 3299

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

Problem 3300

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