2.17.2 Problems 101 to 200

Problem 101

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

Problem 102

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

Problem 103

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

Problem 104

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

Problem 105

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

Problem 106

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

Problem 107

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

Problem 108

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

Problem 109

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

Problem 110

ODE	\[ \boxed {-y+\left (-x +6 y\right ) y^{\prime }=-4 x} \]
program solution	\[ x \left (2 x -y\right )+3 y^{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {c_{1} x -\sqrt {-23 c_{1}^{2} x^{2}+12}}{6 c_{1}} \\ y \left (x \right ) &= \frac {c_{1} x +\sqrt {-23 c_{1}^{2} x^{2}+12}}{6 c_{1}} \\ \end{align*}

Problem 111

ODE	\[ \boxed {2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }=-3 x^{2}} \]
program solution	\[ 2 y^{3}+2 x y^{2}+x^{3} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\frac {\left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}}}{2}+\frac {2 x^{2} c_{1}^{2}}{\left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}}}-c_{1} x}{3 c_{1}} \\ y \left (x \right ) &= \frac {4 i \sqrt {3}\, c_{1}^{2} x^{2}-i \sqrt {3}\, \left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {2}{3}}-4 c_{1}^{2} x^{2}-4 c_{1} x \left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}}-\left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {2}{3}}}{12 \left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}} c_{1}} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) \left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {2}{3}}-4 x \left (i x c_{1} \sqrt {3}+c_{1} x +\left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}}\right ) c_{1}}{12 \left (54-62 x^{3} c_{1}^{3}+6 \sqrt {105 c_{1}^{6} x^{6}-186 x^{3} c_{1}^{3}+81}\right )^{\frac {1}{3}} c_{1}} \\ \end{align*}

Problem 112

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

Problem 113

ODE	\[ \boxed {\frac {y}{x}+\left (\ln \left (x \right )+y^{2}\right ) y^{\prime }=-x^{3}} \]
program solution	\[ \frac {x^{4}}{4}+\ln \left (x \right ) y+\frac {y^{3}}{3} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {2}{3}}-4 \ln \left (x \right )}{2 \left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {i \left (-\left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {2}{3}}-4 \ln \left (x \right )\right ) \sqrt {3}-\left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {2}{3}}+4 \ln \left (x \right )}{4 \left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {i \left (\left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {2}{3}}+4 \ln \left (x \right )\right ) \sqrt {3}-\left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {2}{3}}+4 \ln \left (x \right )}{4 \left (-3 x^{4}-12 c_{1} +\sqrt {64 \ln \left (x \right )^{3}+9 \left (x^{4}+4 c_{1} \right )^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 114

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

Problem 115

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

Problem 116

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

Problem 117

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

Problem 118

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

Problem 119

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

Problem 120

ODE	\[ \boxed {\frac {2 x^{\frac {5}{2}}-3 y^{\frac {5}{3}}}{2 x^{\frac {5}{2}} y^{\frac {2}{3}}}+\frac {\left (-2 x^{\frac {5}{2}}+3 y^{\frac {5}{3}}\right ) y^{\prime }}{3 x^{\frac {3}{2}} y^{\frac {5}{3}}}=0} \]
program solution	\[ y = {\mathrm e}^{\frac {3 \ln \left (x \right )}{2}+\frac {3 c_{1}}{2}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2^{\frac {3}{5}} 3^{\frac {2}{5}} \left (x^{\frac {5}{2}}\right )^{\frac {3}{5}}}{3} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}+\sqrt {5}+1\right )^{3} 2^{\frac {3}{5}} 3^{\frac {2}{5}} \left (x^{\frac {5}{2}}\right )^{\frac {3}{5}}}{192} \\ y \left (x \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}-\sqrt {5}-1\right )^{3} 2^{\frac {3}{5}} 3^{\frac {2}{5}} \left (x^{\frac {5}{2}}\right )^{\frac {3}{5}}}{192} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}-\sqrt {5}+1\right )^{3} 2^{\frac {3}{5}} 3^{\frac {2}{5}} \left (x^{\frac {5}{2}}\right )^{\frac {3}{5}}}{192} \\ y \left (x \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}+\sqrt {5}-1\right )^{3} 2^{\frac {3}{5}} 3^{\frac {2}{5}} \left (x^{\frac {5}{2}}\right )^{\frac {3}{5}}}{192} \\ \frac {x}{y \left (x \right )^{\frac {2}{3}}}+\frac {y \left (x \right )}{x^{\frac {3}{2}}}+c_{1} &= 0 \\ \end{align*}

Problem 121

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

Problem 122

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

Problem 123

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

Problem 124

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

Problem 125

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

Problem 126

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

Problem 127

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

Problem 128

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

Problem 129

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

Problem 130

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

Problem 131

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

Problem 132

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

Problem 133

ODE	\[ \boxed {y^{\prime }-y^{2}-x^{2} y^{4}=x^{2}+1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 134

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

Problem 135

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

Problem 136

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

Problem 137

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

Problem 138

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

Problem 139

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

Problem 140

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

Problem 141

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

Problem 142

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

Problem 143

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

Problem 144

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

Problem 145

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

Problem 146

ODE	\[ \boxed {9 \sqrt {x}\, y^{\frac {4}{3}}-12 x^{\frac {1}{5}} y^{\frac {3}{2}}+\left (8 x^{\frac {3}{2}} y^{\frac {1}{3}}-15 x^{\frac {6}{5}} \sqrt {y}\right ) y^{\prime }=0} \]
program solution	\[ 6 y^{\frac {4}{3}} x^{\frac {3}{2}}-10 y^{\frac {3}{2}} x^{\frac {6}{5}} = c_{1} \] Verified OK.
Maple solution	\[ 125 y \left (x \right )^{\frac {9}{2}} x^{\frac {18}{5}}-225 y \left (x \right )^{\frac {13}{3}} x^{\frac {39}{10}}+135 y \left (x \right )^{\frac {25}{6}} x^{\frac {21}{5}}-27 y \left (x \right )^{4} x^{\frac {9}{2}}-c_{1} = 0 \]

Problem 147

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

Problem 148

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

Problem 149

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

Problem 150

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

Problem 151

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

Problem 152

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

Problem 153

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

Problem 154

ODE	\[ \boxed {y^{\prime }-\frac {x +3 y}{-3 x +y}=0} \]
program solution	\[ -\frac {x \left (x +6 y\right )}{2}+\frac {y^{2}}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {3 c_{1} x -\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \left (x \right ) &= \frac {3 c_{1} x +\sqrt {10 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

Problem 155

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

Problem 156

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

Problem 157

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

Problem 158

ODE	\[ \boxed {y^{\prime \prime }-9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 15] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{3 x}-3 \,{\mathrm e}^{-3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -3 \,{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{3 x} \]

Problem 159

ODE	\[ \boxed {y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 8] \end {align*}
program solution	\[ y = 3 \cos \left (2 x \right )+4 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 4 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

Problem 160

ODE	\[ \boxed {y^{\prime \prime }+25 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 10, y^{\prime }\left (0\right ) = -10] \end {align*}
program solution	\[ y = 10 \cos \left (5 x \right )-2 \sin \left (5 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 \sin \left (5 x \right )+10 \cos \left (5 x \right ) \]

Problem 161

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

Problem 162

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 7, y^{\prime }\left (0\right ) = -1] \end {align*}
program solution	\[ y = 4 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{-3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (4 \,{\mathrm e}^{5 x}+3\right ) {\mathrm e}^{-3 x} \]

Problem 163

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 8] \end {align*}
program solution	\[ y = 6-8 \,{\mathrm e}^{-x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 6-8 \,{\mathrm e}^{-x} \]

Problem 164

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = -2] \end {align*}
program solution	N/A
Maple solution	\[ y \left (x \right ) = \frac {14}{3}-\frac {2 \,{\mathrm e}^{3 x}}{3} \]

Problem 165

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

Problem 166

ODE	\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 13] \end {align*}
program solution	\[ y = {\mathrm e}^{5 x} \left (3-2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{5 x} \left (3-2 x \right ) \]

Problem 167

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

Problem 168

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

Problem 169

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

Problem 170

ODE	\[ \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 10, y^{\prime }\left (2\right ) = 15] \end {align*}
program solution	\[ y = \frac {3 x^{5}-16}{x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {16}{x^{3}}+3 x^{2} \]

Problem 171

ODE	\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 7, y^{\prime }\left (1\right ) = 2] \end {align*}
program solution	\[ y = \left (-5 \ln \left (x \right )+7\right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (7-5 \ln \left (x \right )\right ) \]

Problem 172

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

Problem 173

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

Problem 174

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }-15 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{3 x}}{8} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{8 x}+c_{1} \right ) {\mathrm e}^{-5 x} \]

Problem 175

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

Problem 176

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

Problem 177

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

Problem 178

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

Problem 179

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

Problem 180

ODE	\[ \boxed {9 y^{\prime \prime }-12 y^{\prime }+4 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {2 x}{3}}+c_{2} x \,{\mathrm e}^{\frac {2 x}{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {2 x}{3}} \left (c_{2} x +c_{1} \right ) \]

Problem 181

ODE	\[ \boxed {6 y^{\prime \prime }-7 y^{\prime }-20 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-\frac {4 x}{3}}+\frac {6 c_{2} {\mathrm e}^{\frac {5 x}{2}}}{23} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{\frac {23 x}{6}}+c_{2} \right ) {\mathrm e}^{-\frac {4 x}{3}} \]

Problem 182

ODE	\[ \boxed {35 y^{\prime \prime }-y^{\prime }-12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-\frac {4 x}{7}}+\frac {35 c_{2} {\mathrm e}^{\frac {3 x}{5}}}{41} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{\frac {41 x}{35}}+c_{2} \right ) {\mathrm e}^{-\frac {4 x}{7}} \]

Problem 183

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

Problem 184

ODE	\[ \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y=0} \]
program solution	\[ y = \frac {c_{1}}{x^{4}}+\frac {c_{2} x^{3}}{7} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{2} x^{7}+c_{1}}{x^{4}} \]

Problem 185

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

Problem 186

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

Problem 187

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

Problem 188

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

Problem 189

ODE	\[ \boxed {y^{\prime \prime }-4 y=12} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 10] \end {align*}
program solution	\[ y = -3+4 \,{\mathrm e}^{2 x}-{\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 4 \,{\mathrm e}^{2 x}-{\mathrm e}^{-2 x}-3 \]

Problem 190

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=6} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 11] \end {align*}
program solution	\[ y = -2+4 \,{\mathrm e}^{3 x}+{\mathrm e}^{-x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x}+4 \,{\mathrm e}^{3 x}-2 \]

Problem 191

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 8] \end {align*}
program solution	\[ y = 1+3 \cos \left (x \right ) {\mathrm e}^{x}+4 \sin \left (x \right ) {\mathrm e}^{x}+x \] Verified OK.
Maple solution	\[ y \left (x \right ) = x +1+\left (4 \sin \left (x \right )+3 \cos \left (x \right )\right ) {\mathrm e}^{x} \]

Problem 192

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

Problem 193

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

Problem 194

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

Problem 195

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

Problem 196

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

Problem 197

ODE	\[ \boxed {y^{\prime \prime }+3 y^{\prime }-10 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{2 x}}{7} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{7 x}+c_{1} \right ) {\mathrm e}^{-5 x} \]

Problem 198

ODE	\[ \boxed {2 y^{\prime \prime }-7 y^{\prime }+3 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+\frac {2 c_{2} {\mathrm e}^{3 x}}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{3 x} \]

Problem 199

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

Problem 200

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