2.17.32 Problems 3101 to 3200

Problem 3101

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

Problem 3102

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

Problem 3103

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

Problem 3104

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

Problem 3105

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

Problem 3106

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

Problem 3107

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

Problem 3108

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

Problem 3109

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

Problem 3110

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

Problem 3111

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

Problem 3112

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

Problem 3113

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

Problem 3114

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

Problem 3115

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

Problem 3116

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

Problem 3117

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

Problem 3118

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

Problem 3119

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

Problem 3120

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

Problem 3121

ODE	\[ \boxed {\left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+{\mathrm e}^{x} y-2 x y^{3}=0} \]
program solution	\[ y \left (-x^{2} y^{2}+{\mathrm e}^{x}\right ) = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {2}{3}}+12 \,{\mathrm e}^{x}}{6 \left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {-i \sqrt {3}\, \left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {2}{3}}+12 i {\mathrm e}^{x} \sqrt {3}-\left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {2}{3}}-12 \,{\mathrm e}^{x}}{12 \left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= -\frac {-i \sqrt {3}\, \left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {2}{3}}+12 i {\mathrm e}^{x} \sqrt {3}+\left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {2}{3}}+12 \,{\mathrm e}^{x}}{12 \left (108 c_{1} x +12 \sqrt {81 c_{1}^{2} x^{2}-12 \,{\mathrm e}^{3 x}}\right )^{\frac {1}{3}} x} \\ \end{align*}

Problem 3122

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

Problem 3123

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

Problem 3124

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

Problem 3125

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

Problem 3126

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

Problem 3127

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

Problem 3128

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

Problem 3129

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

Problem 3130

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

Problem 3131

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

Problem 3132

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

Problem 3133

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

Problem 3134

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

Problem 3135

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

Problem 3136

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

Problem 3137

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

Problem 3138

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

Problem 3139

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

Problem 3140

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

Problem 3141

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

Problem 3142

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

Problem 3143

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

Problem 3144

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

Problem 3145

ODE	\[ \boxed {y^{2} y^{\prime }-3 y^{6}=2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {\tan \left (3 x \sqrt {6}\right )^{\frac {1}{3}} 6^{\frac {1}{6}} 9^{\frac {1}{3}}}{3} \] Verified OK. \[ y = \frac {i \tan \left (3 x \sqrt {6}\right )^{\frac {1}{3}} 6^{\frac {1}{6}} 3^{\frac {1}{6}}}{2}-\frac {\tan \left (3 x \sqrt {6}\right )^{\frac {1}{3}} 6^{\frac {1}{6}} 3^{\frac {2}{3}}}{6} \] Verified OK. \[ y = -\frac {i \tan \left (3 x \sqrt {6}\right )^{\frac {1}{3}} 6^{\frac {1}{6}} 3^{\frac {1}{6}}}{2}-\frac {\tan \left (3 x \sqrt {6}\right )^{\frac {1}{3}} 6^{\frac {1}{6}} 3^{\frac {2}{3}}}{6} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {3^{\frac {5}{6}} 2^{\frac {1}{6}} \tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}}}{3} \\ y \left (x \right ) &= \frac {\tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}} \left (3 i 3^{\frac {1}{6}}-3^{\frac {2}{3}}\right ) 6^{\frac {1}{6}}}{6} \\ y \left (x \right ) &= -\frac {\tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}} \left (3 i 3^{\frac {1}{6}}+3^{\frac {2}{3}}\right ) 6^{\frac {1}{6}}}{6} \\ \end{align*}

Problem 3146

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

Problem 3147

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

Problem 3148

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

Problem 3149

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

Problem 3150

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

Problem 3151

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

Problem 3152

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

Problem 3153

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

Problem 3154

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

Problem 3155

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

Problem 3156

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

Problem 3157

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

Problem 3158

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

Problem 3159

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

Problem 3160

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

Problem 3161

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

Problem 3162

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

Problem 3163

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

Problem 3164

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

Problem 3165

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

Problem 3166

ODE	\[ \boxed {-x y^{2}-2 y-\left (y x^{2}+2 x \right ) y^{\prime }=-2 x^{2}-3} \]
program solution	\[ \frac {2 x^{3}}{3}-\frac {x^{2} y^{2}}{2}+\left (-2 y+3\right ) x = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-6-\sqrt {12 x^{3}+18 c_{1} +54 x +36}}{3 x} \\ y \left (x \right ) &= \frac {-6+\sqrt {12 x^{3}+18 c_{1} +54 x +36}}{3 x} \\ \end{align*}

Problem 3167

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

Problem 3168

ODE	\[ \boxed {3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime }=0} \]
program solution	\[ y x \left (x^{2}-3\right )+4 y^{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{8}+\frac {3 x}{8}-\frac {\sqrt {x^{6}-6 x^{4}+9 x^{2}-16 c_{1}}}{8} \\ y \left (x \right ) &= -\frac {x^{3}}{8}+\frac {3 x}{8}+\frac {\sqrt {x^{6}-6 x^{4}+9 x^{2}-16 c_{1}}}{8} \\ \end{align*}

Problem 3169

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

Problem 3170

ODE	\[ \boxed {2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime }=0} \]
program solution	\[ y x^{2}+2 x^{3}+y \,{\mathrm e}^{-x^{2}}+y^{3} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {12^{\frac {1}{3}} \left (-\left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {2}{3}} {\mathrm e}^{-x^{2}}+\left ({\mathrm e}^{x^{2}} x^{2}+1\right ) 12^{\frac {1}{3}}\right )}{6 \left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {3^{\frac {1}{3}} \left ({\mathrm e}^{-x^{2}} \left (1+i \sqrt {3}\right ) \left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {2}{3}}+\left ({\mathrm e}^{x^{2}} x^{2}+1\right ) 2^{\frac {2}{3}} \left (i 3^{\frac {5}{6}}-3^{\frac {1}{3}}\right )\right ) 2^{\frac {2}{3}}}{12 \left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {3^{\frac {1}{3}} \left (\left (i \sqrt {3}-1\right ) {\mathrm e}^{-x^{2}} \left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {2}{3}}+\left ({\mathrm e}^{x^{2}} x^{2}+1\right ) \left (i 3^{\frac {5}{6}}+3^{\frac {1}{3}}\right ) 2^{\frac {2}{3}}\right ) 2^{\frac {2}{3}}}{12 \left (\sqrt {3}\, {\mathrm e}^{2 x^{2}} \sqrt {\left (4+\left (112 x^{6}+108 c_{1} x^{3}+27 c_{1}^{2}\right ) {\mathrm e}^{3 x^{2}}+12 \,{\mathrm e}^{2 x^{2}} x^{4}+12 \,{\mathrm e}^{x^{2}} x^{2}\right ) {\mathrm e}^{-x^{2}}}-18 \,{\mathrm e}^{3 x^{2}} \left (x^{3}+\frac {c_{1}}{2}\right )\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 3171

ODE	\[ \boxed {y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }=-3} \]
program solution	\[ -\frac {\sin \left (2 x \right ) y^{2}}{2}+x \left (y^{2}+y+3\right ) = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {x +\sqrt {\left (2 c_{1} +6 x \right ) \sin \left (2 x \right )-11 x^{2}-4 c_{1} x}}{\sin \left (2 x \right )-2 x} \\ y \left (x \right ) &= \frac {x -\sqrt {\left (2 c_{1} +6 x \right ) \sin \left (2 x \right )-11 x^{2}-4 c_{1} x}}{\sin \left (2 x \right )-2 x} \\ \end{align*}

Problem 3172

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

Problem 3173

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

Problem 3174

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

Problem 3175

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

Problem 3176

ODE	\[ \boxed {y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }=0} \]
program solution	\[ y \ln \left (x \right )+\frac {y^{3}}{3} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}}-4 \ln \left (x \right )}{2 \left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {i \left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}} \sqrt {3}+4 i \ln \left (x \right ) \sqrt {3}+\left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}}-4 \ln \left (x \right )}{4 \left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {i \left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}} \sqrt {3}+4 i \ln \left (x \right ) \sqrt {3}-\left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}}+4 \ln \left (x \right )}{4 \left (-12 c_{1} +4 \sqrt {4 \ln \left (x \right )^{3}+9 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 3177

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

Problem 3178

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 3179

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

Problem 3180

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

Problem 3181

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

Problem 3182

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

Problem 3183

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

Problem 3184

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

Problem 3185

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

Problem 3186

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

Problem 3187

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

Problem 3188

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

Problem 3189

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

Problem 3190

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

Problem 3191

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

Problem 3192

ODE	\[ \boxed {2 y^{4} x -y+\left (4 y^{3} x^{3}-x \right ) y^{\prime }=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 3193

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

Problem 3194

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

Problem 3195

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

Problem 3196

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

Problem 3197

ODE	\[ \boxed {2 y x^{3}+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime }=0} \]
program solution	\[ -2 \ln \left (y\right )+\frac {3 \ln \left (-x^{3}+4 y^{2}\right )}{2} = \frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-x^{\frac {3}{2}} \operatorname {RootOf}\left (-16+x^{7} c_{1} \textit {\_Z}^{12}-4 c_{1} x^{\frac {11}{2}} \textit {\_Z}^{10}+6 c_{1} x^{4} \textit {\_Z}^{8}+\left (128 x^{\frac {9}{2}}-4 x^{\frac {5}{2}} c_{1} \right ) \textit {\_Z}^{6}+\left (-192 x^{3}+c_{1} x \right ) \textit {\_Z}^{4}+96 x^{\frac {3}{2}} \textit {\_Z}^{2}\right )^{2}+1}{2 \operatorname {RootOf}\left (-16+x^{7} c_{1} \textit {\_Z}^{12}-4 c_{1} x^{\frac {11}{2}} \textit {\_Z}^{10}+6 c_{1} x^{4} \textit {\_Z}^{8}+\left (128 x^{\frac {9}{2}}-4 x^{\frac {5}{2}} c_{1} \right ) \textit {\_Z}^{6}+\left (-192 x^{3}+c_{1} x \right ) \textit {\_Z}^{4}+96 x^{\frac {3}{2}} \textit {\_Z}^{2}\right )^{2}} \]

Problem 3198

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

Problem 3199

ODE	\[ \boxed {\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \arctan \left (-\frac {\sqrt {\frac {\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, \frac {\sqrt {\frac {\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}\, \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right )}{36 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\sqrt {\frac {\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, -\frac {\sqrt {\frac {\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}\, \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right )}{36 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= \arctan \left (-\frac {\sqrt {\frac {i \left (-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, \frac {\left (-i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {\frac {i \left (-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{72 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\sqrt {\frac {i \left (-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, \frac {\sqrt {\frac {i \left (-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}\, \left (i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}+\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right )}{72 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= \arctan \left (-\frac {\sqrt {\frac {i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, \frac {\sqrt {\frac {i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}\, \left (i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right )}{72 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\sqrt {\frac {i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{6}, \frac {\left (-i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}+\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}-12 x^{2}\right ) \sqrt {\frac {i \left (\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}\right ) \sqrt {3}-\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {2}{3}}+12 x^{2}}{\left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}}}{72 x \left (108 x^{2}+12 \sqrt {3}\, \sqrt {4 x^{6}+27 x^{4}}\right )^{\frac {1}{3}}}\right ) \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 3200

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