2.17.118 Problems 11701 to 11800

Problem 11701

ODE	\[ \boxed {2 y^{2} x +y+\left (2 y^{3}-x \right ) y^{\prime }=0} \]
program solution	\[ \frac {x \left (x y+1\right )}{y}+y^{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-12 x^{2}-12 c_{1} +\left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {2}{3}}}{6 \left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {\left (\frac {i \sqrt {3}}{12}+\frac {1}{12}\right ) \left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {2}{3}}+\left (x^{2}+c_{1} \right ) \left (i \sqrt {3}-1\right )}{\left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {2}{3}}}{12}+\left (x^{2}+c_{1} \right ) \left (1+i \sqrt {3}\right )}{\left (-108 x +12 \sqrt {12 x^{6}+36 x^{4} c_{1} +\left (36 c_{1}^{2}+81\right ) x^{2}+12 c_{1}^{3}}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 11702

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

Problem 11703

ODE	\[ \boxed {8 y^{3} x^{2}-2 y^{4}+\left (5 y^{2} x^{3}-8 y^{3} x \right ) y^{\prime }=0} \]
program solution	\[ \frac {5 \ln \left (y\right )}{18}+\frac {\ln \left (-x^{2}+y\right )}{6} = -\frac {\ln \left (x \right )}{9}+c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \operatorname {RootOf}\left (x^{6} \textit {\_Z}^{48}-x^{6} \textit {\_Z}^{30}-c_{1} \right )^{18} x^{2} \\ \end{align*}

Problem 11704

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

Problem 11705

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

Problem 11706

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

Problem 11707

ODE	\[ \boxed {-4 y-\left (x +5 y+3\right ) y^{\prime }=-10 x -12} \]
program solution	\[ \frac {2 \ln \left (y-x -1\right )}{15}+\frac {\ln \left (2 x +y+3\right )}{5} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-3 x -4\right ) {\operatorname {RootOf}\left (-1+\left (243 c_{1} x^{5}+1620 x^{4} c_{1} +4320 c_{1} x^{3}+5760 c_{1} x^{2}+3840 c_{1} x +1024 c_{1} \right ) \textit {\_Z}^{25}+\left (1458 c_{1} x^{5}+9720 x^{4} c_{1} +25920 c_{1} x^{3}+34560 c_{1} x^{2}+23040 c_{1} x +6144 c_{1} \right ) \textit {\_Z}^{20}+\left (2187 c_{1} x^{5}+14580 x^{4} c_{1} +38880 c_{1} x^{3}+51840 c_{1} x^{2}+34560 c_{1} x +9216 c_{1} \right ) \textit {\_Z}^{15}\right )}^{5}}{3}-2 x -3 \]

Problem 11708

ODE	\[ \boxed {4 y+\left (4 x +2 y+2\right ) y^{\prime }=-6 x -1} \] With initial conditions \begin {align*} \left [y \left (\frac {1}{2}\right ) = 3\right ] \end {align*}
program solution	\[ y^{2}+\left (4 x +2\right ) y+3 x^{2}+x = {\frac {89}{4}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 x -1+\frac {\sqrt {4 x^{2}+12 x +93}}{2} \]

Problem 11709

ODE	\[ \boxed {-y+\left (x +y+2\right ) y^{\prime }=-3 x +6} \] With initial conditions \begin {align*} [y \left (2\right ) = -2] \end {align*}
program solution	\[ -\frac {\ln \left (3 x^{2}+y^{2}-6 x +6 y+12\right )}{2}-\frac {\sqrt {3}\, \arctan \left (\frac {\left (y+3\right ) \sqrt {3}}{-3+3 x}\right )}{3} = -\ln \left (2\right )-\frac {\pi \sqrt {3}}{18} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -3-\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-3 \sqrt {3}\, \ln \left (3\right )+6 \sqrt {3}\, \ln \left (2\right )-3 \sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (-1+x \right )^{2}\right )+\pi +6 \textit {\_Z} \right )\right ) \left (-1+x \right ) \]

Problem 11710

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

Problem 11711

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

Problem 11712

ODE	\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y={\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 7] \end {align*}
program solution	\[ y = \frac {\left ({\mathrm e}^{4 x}+260 \,{\mathrm e}^{x}-201\right ) {\mathrm e}^{-3 x}}{12} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{4 x}+260 \,{\mathrm e}^{x}-201\right ) {\mathrm e}^{-3 x}}{12} \]

Problem 11713

ODE	\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y={\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (1\right ) = 7] \end {align*}
program solution	\[ y = -\frac {\left (354 \,{\mathrm e}^{1-x}-252 \,{\mathrm e}^{3}+12 \,{\mathrm e}^{3 x +1}+171 \,{\mathrm e}^{4}-9 \,{\mathrm e}^{3 x}+2 \,{\mathrm e}^{-x +5}-171 \,{\mathrm e}^{4-x}+252 \,{\mathrm e}^{-x +3}-236 \,{\mathrm e}^{-x +2}-4 \,{\mathrm e}^{3 x +2}-2 \,{\mathrm e}^{5}+354 \,{\mathrm e}-531\right ) {\mathrm e}^{-2 x}}{48 \,{\mathrm e}^{2}-144 \,{\mathrm e}+108} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-{\mathrm e}^{4-x}+84 \,{\mathrm e}^{3-x}+{\mathrm e}^{4}+2 \,{\mathrm e}^{3 x +1}-84 \,{\mathrm e}^{3}+118 \,{\mathrm e}^{1-x}-3 \,{\mathrm e}^{3 x}-177\right ) {\mathrm e}^{-2 x}}{24 \,{\mathrm e}-36} \]

Problem 11714

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

Problem 11715

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

Problem 11716

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

Problem 11717

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 ) = 2] \end {align*}
program solution	\[ y = -x^{2}+4 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x^{2}+4 x \]

Problem 11718

ODE	\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -4 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 3, y^{\prime }\left (2\right ) = -1] \end {align*}
program solution	\[ y = \frac {x^{4}+32}{4 x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{4}+32}{4 x^{2}} \]

Problem 11719

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

Problem 11720

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{3 x} c_{2} +{\mathrm e}^{4 x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{4 x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{3 x} \]

Problem 11721

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

Problem 11722

ODE	\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
program solution	\[ y = c_{1} x +\frac {1}{3} c_{2} x^{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (c_{1} x^{3}+c_{2} \right ) \]

Problem 11723

ODE	\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x +1 \end {align*}
program solution	\[ y = \left (x +1\right ) c_{1} +c_{2} \left (x +1\right ) \left (\frac {1}{2} x^{2}+x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+x \right ) \left (c_{1} +c_{2} \left (1+x \right )^{2}\right ) \]

Problem 11724

ODE	\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
program solution	\[ y = c_{1} x +c_{2} x \left (x +\frac {1}{x}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{2}+c_{1} x +c_{2} \]

Problem 11725

ODE	\[ \boxed {\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+y \left (x +1\right )=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
program solution	\[ y = c_{1} x +c_{2} \left (x -1\right ) {\mathrm e}^{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{x} \left (-1+x \right ) \]

Problem 11726

ODE	\[ \boxed {\left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 x} \end {align*}
program solution	\[ y = c_{1} {\mathrm e}^{2 x}-c_{2} {\mathrm e}^{2 x} \left (x +1\right ) {\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} x +c_{1} \]

Problem 11727

ODE	\[ \boxed {\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
program solution	\[ y = c_{1} x^{2}+c_{2} x \,{\mathrm e}^{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (c_{2} {\mathrm e}^{x}+c_{1} x \right ) \]

Problem 11728

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

Problem 11729

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=2-12 x +6 \,{\mathrm e}^{x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{2} +3 \,{\mathrm e}^{x}-\frac {4}{3}-2 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+3 \,{\mathrm e}^{x}-2 x -\frac {4}{3} \]

Problem 11730

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

Problem 11731

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

Problem 11732

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

Problem 11733

ODE	\[ \boxed {3 y^{\prime \prime }-14 y^{\prime }-5 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-\frac {x}{3}}+\frac {3 c_{2} {\mathrm e}^{5 x}}{16} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{5 x}+c_{2} {\mathrm e}^{-\frac {x}{3}} \]

Problem 11734

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

Problem 11735

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{3 x} c_{2} +{\mathrm e}^{4 x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{4 x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{3 x} \]

Problem 11736

ODE	\[ \boxed {y^{\prime \prime }-8 y^{\prime }+16 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{4 x}+c_{2} x \,{\mathrm e}^{4 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{4 x} \left (c_{2} x +c_{1} \right ) \]

Problem 11737

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 11738

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x} \cos \left (3 x \right )+\frac {c_{2} {\mathrm e}^{2 x} \sin \left (3 x \right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )\right ) \]

Problem 11739

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+25 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-3 x} \cos \left (4 x \right )+\frac {c_{2} {\mathrm e}^{-3 x} \sin \left (4 x \right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (c_{1} \sin \left (4 x \right )+c_{2} \cos \left (4 x \right )\right ) \]

Problem 11740

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

Problem 11741

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

Problem 11742

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

Problem 11743

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

Problem 11744

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

Problem 11745

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

Problem 11746

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

Problem 11747

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y=0} \]
program solution	\[ y = {\mathrm e}^{-2 i x} c_{1} +x \,{\mathrm e}^{-2 i x} c_{2} +{\mathrm e}^{2 i x} c_{3} +x \,{\mathrm e}^{2 i x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{4} x +c_{2} \right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_{3} x +c_{1} \right ) \]

Problem 11748

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

Problem 11749

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

Problem 11750

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

Problem 11751

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+x \,{\mathrm e}^{-2 x} c_{2} +{\mathrm e}^{\left (-i \sqrt {2}-1\right ) x} c_{3} +{\mathrm e}^{\left (i \sqrt {2}-1\right ) x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{4} {\mathrm e}^{-x} \cos \left (x \sqrt {2}\right )+c_{3} {\mathrm e}^{-x} \sin \left (x \sqrt {2}\right )+{\mathrm e}^{-2 x} \left (c_{2} x +c_{1} \right ) \]

Problem 11752

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

Problem 11753

ODE	\[ \boxed {y^{\left (5\right )}=0} \]
program solution	\[ y = c_{5} x^{4}+c_{4} x^{3}+x^{2} c_{3} +c_{2} x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{24} x^{4} c_{1} +\frac {1}{6} c_{2} x^{3}+\frac {1}{2} c_{3} x^{2}+c_{4} x +c_{5} \]

Problem 11754

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime }-12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{4 x}+{\mathrm e}^{-3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (2 \,{\mathrm e}^{7 x}+1\right ) {\mathrm e}^{-3 x} \]

Problem 11755

ODE	\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -4, y^{\prime }\left (0\right ) = 2] \end {align*}
program solution	\[ y = -6 \,{\mathrm e}^{-2 x}+2 \,{\mathrm e}^{-5 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \,{\mathrm e}^{-5 x}-6 \,{\mathrm e}^{-2 x} \]

Problem 11756

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }+8 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 6] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{4 x}-{\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \,{\mathrm e}^{4 x}-{\mathrm e}^{2 x} \]

Problem 11757

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

Problem 11758

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

Problem 11759

ODE	\[ \boxed {4 y^{\prime \prime }-12 y^{\prime }+9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 9] \end {align*}
program solution	\[ y = {\mathrm e}^{\frac {3 x}{2}} \left (4+3 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x}{2}} \left (3 x +4\right ) \]

Problem 11760

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 7] \end {align*}
program solution	\[ y = {\mathrm e}^{-2 x} \left (3+13 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (3+13 x \right ) \]

Problem 11761

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

Problem 11762

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+29 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 5] \end {align*}
program solution	\[ y = {\mathrm e}^{2 x} \sin \left (5 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (5 x \right ) \]

Problem 11763

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+58 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 5] \end {align*}
program solution	\[ y = -\frac {{\mathrm e}^{-3 x} \left (7 \cos \left (7 x \right )-2 \sin \left (7 x \right )\right )}{7} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-3 x} \left (2 \sin \left (7 x \right )-7 \cos \left (7 x \right )\right )}{7} \]

Problem 11764

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

Problem 11765

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

Problem 11766

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

Problem 11767

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

Problem 11768

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

Problem 11769

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

Problem 11770

ODE	\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -8, y^{\prime \prime }\left (0\right ) = -4] \end {align*}
program solution	\[ y = \frac {\left (6 x -23\right ) {\mathrm e}^{2 x}}{9}+\frac {32 \,{\mathrm e}^{-x}}{9} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (6 x -23\right ) {\mathrm e}^{2 x}}{9}+\frac {32 \,{\mathrm e}^{-x}}{9} \]

Problem 11771

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

Problem 11772

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

Problem 11773

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-3 x}+{\mathrm e}^{\left (1-2 i\right ) x} c_{3} +{\mathrm e}^{\left (1+2 i\right ) x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{3} {\mathrm e}^{4 x} \sin \left (2 x \right )+c_{4} {\mathrm e}^{4 x} \cos \left (2 x \right )+c_{2} {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-3 x} \]

Problem 11774

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }+8 y=4 x^{2}} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right )+\frac {2 c_{2} \sin \left (\frac {\sqrt {23}\, x}{2}\right ) {\mathrm e}^{\frac {3 x}{2}} \sqrt {23}}{23}+\frac {x^{2}}{2}+\frac {3 x}{8}+\frac {1}{64} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {23}\, x}{2}\right ) c_{2} +{\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right ) c_{1} +\frac {x^{2}}{2}+\frac {3 x}{8}+\frac {1}{64} \]

Problem 11775

ODE	\[ \boxed {y^{\prime \prime }-2 y^{\prime }-8 y=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{4 x}}{6}-3 \,{\mathrm e}^{-3 x}-\frac {{\mathrm e}^{2 x}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 c_{2} {\mathrm e}^{7 x}-{\mathrm e}^{5 x}+2 c_{1} {\mathrm e}^{x}-6\right ) {\mathrm e}^{-3 x}}{2} \]

Problem 11776

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

Problem 11777

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=10 \sin \left (4 x \right )} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )\right )-\frac {4 \cos \left (4 x \right )}{13}-\frac {7 \sin \left (4 x \right )}{13} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (x \right ) c_{1} -\frac {7 \sin \left (4 x \right )}{13}-\frac {4 \cos \left (4 x \right )}{13} \]

Problem 11778

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }+4 y=\cos \left (4 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right )+\frac {c_{2} \sin \left (\sqrt {3}\, x \right ) {\mathrm e}^{-x} \sqrt {3}}{3}-\frac {3 \cos \left (4 x \right )}{52}+\frac {\sin \left (4 x \right )}{26} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) c_{1} +\frac {\sin \left (4 x \right )}{26}-\frac {3 \cos \left (4 x \right )}{52} \]

Problem 11779

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

Problem 11780

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+5 y=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{-x}}{4}+\frac {{\mathrm e}^{x}}{6}+\frac {{\mathrm e}^{5 x}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{10 x}+{\mathrm e}^{6 x}+6 c_{1} {\mathrm e}^{4 x}+6 c_{2} \right ) {\mathrm e}^{-5 x}}{6} \]

Problem 11781

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

Problem 11782

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

Problem 11783

ODE	\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y=8 x \,{\mathrm e}^{-2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{\left (-2-i\right ) x} c_{2} +{\mathrm e}^{\left (-2+i\right ) x} c_{3} -2 x \,{\mathrm e}^{-2 x}-\frac {{\mathrm e}^{-2 x}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 c_{2} \cos \left (x \right )+2 c_{3} \sin \left (x \right )-4 x -1\right ) {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{2 x} c_{1} \]

Problem 11784

ODE	\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y=5 \sin \left (2 x \right )+10 x^{2}+3 x +7} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{\left (-1+2 i\right ) x} c_{2} +{\mathrm e}^{\left (-1-2 i\right ) x} c_{3} +\frac {2 \cos \left (2 x \right )}{17}-\frac {9 \sin \left (2 x \right )}{17}-4-3 x -2 x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (17 c_{3} {\mathrm e}^{-x}-9\right ) \sin \left (2 x \right )}{17}+c_{2} {\mathrm e}^{-x} \cos \left (2 x \right )-2 x^{2}+c_{1} {\mathrm e}^{x}-3 x +\frac {2 \cos \left (2 x \right )}{17}-4 \]

Problem 11785

ODE	\[ \boxed {4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y=3 x^{3}-8 x} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{\frac {x}{2}} c_{2} +{\mathrm e}^{\frac {3 x}{2}} c_{3} +x^{3}+5 x^{2}+22 x +42 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}}+c_{3} {\mathrm e}^{\frac {5 x}{2}}+\left (x^{3}+5 x^{2}+22 x +42\right ) {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-x} \]

Problem 11786

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11} \]
program solution	\[ y = c_{1} {\mathrm e}^{-3 x}+\frac {c_{2} {\mathrm e}^{2 x}}{5}+2-\frac {2 \,{\mathrm e}^{2 x}}{5}-3 \,{\mathrm e}^{3 x}+x +2 \,{\mathrm e}^{2 x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (\left (2 x +c_{1} -\frac {2}{5}\right ) {\mathrm e}^{5 x}+\left (x +2\right ) {\mathrm e}^{3 x}+c_{2} -3 \,{\mathrm e}^{6 x}\right ) \]

Problem 11787

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

Problem 11788

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

Problem 11789

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x}+{\mathrm e}^{2 x} c_{3} +3 \,{\mathrm e}^{2 x} x -{\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (3 x +c_{3} -4\right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}-{\mathrm e}^{3 x} \]

Problem 11790

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

Problem 11791

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x} \]
program solution	\[ y = c_{2} x +c_{1} +c_{3} {\mathrm e}^{x}+{\mathrm e}^{2 x} c_{4} +\frac {{\mathrm e}^{-x}}{2}+\frac {3 \,{\mathrm e}^{2 x} x}{2}-\frac {9 x^{2}}{4}-\frac {x^{3}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (6 x +c_{1} -12\right ) {\mathrm e}^{2 x}}{4}-\frac {x^{3}}{2}-\frac {9 x^{2}}{4}+c_{3} x +c_{2} {\mathrm e}^{x}+c_{4} +\frac {{\mathrm e}^{-x}}{2} \]

Problem 11792

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{3} +4 \,{\mathrm e}^{2 x} x +{\mathrm e}^{4 x}+\frac {3 x \,{\mathrm e}^{x}}{4}+\frac {{\mathrm e}^{x} x^{2}}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (4 x +c_{2} \right ) {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x}+{\mathrm e}^{4 x}+\frac {\left (2 x^{2}+8 c_{1} +6 x +7\right ) {\mathrm e}^{x}}{8} \]

Problem 11793

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

Problem 11794

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

Problem 11795

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

Problem 11796

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9} \]
program solution	\[ y = c_{2} x +c_{1} +c_{3} {\mathrm e}^{x}+{\mathrm e}^{-3 x} c_{4} +\frac {{\mathrm e}^{3 x}}{27}-9 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x} x^{2}-\frac {19 x^{2}}{6}-\frac {4 x^{3}}{3}-\frac {x^{4}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (\left (x^{4}+\frac {8}{3} x^{3}+\frac {19}{3} x^{2}-2 c_{3} x -2 c_{4} \right ) {\mathrm e}^{3 x}+\left (-4 x^{2}+18 x -2 c_{2} -\frac {57}{2}\right ) {\mathrm e}^{4 x}-\frac {2 c_{1}}{9}-\frac {2 \,{\mathrm e}^{6 x}}{27}\right ) {\mathrm e}^{-3 x}}{2} \]

Problem 11797

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y=5 \sin \left (x \right )-12 \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{2} +{\mathrm e}^{i x} c_{3} +{\mathrm e}^{-i x} c_{4} +\frac {27}{65}+\frac {\left (\cos \left (x \right )-\sin \left (x \right )\right ) \left (\int \left (24 \cos \left (x \right )-5\right ) \sin \left (x \right )^{2}d x \right )}{10}+\frac {\left (-\cos \left (x \right )-\sin \left (x \right )\right ) \left (\int \left (24 \cos \left (x \right )-5\right ) \sin \left (x \right ) \cos \left (x \right )d x \right )}{10}-\frac {54 \cos \left (x \right )^{2}}{65}+\frac {3 \left (13-56 \sin \left (x \right )\right ) \cos \left (x \right )}{260}+\frac {\sin \left (x \right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {5 \cos \left (2 x \right )}{13}+c_{3} {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{3 x}+\frac {\sin \left (2 x \right )}{13}+\frac {\left (-2-5 x +20 c_{1} \right ) \cos \left (x \right )}{20}+\frac {\left (1+x +4 c_{2} \right ) \sin \left (x \right )}{4} \]

Problem 11798

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=9 x^{2}+4} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 8] \end {align*}
program solution	\[ y = 10+3 x^{2}+2 \,{\mathrm e}^{3 x}-6 \,{\mathrm e}^{x}+8 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -6 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{3 x}+3 x^{2}+8 x +10 \]

Problem 11799

ODE	\[ \boxed {y^{\prime \prime }+5 y^{\prime }+4 y=16 x +20 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
program solution	\[ y = -5+2 \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-x}+4 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \,{\mathrm e}^{-x}-5+2 \,{\mathrm e}^{x}+4 x \]

Problem 11800

ODE	\[ \boxed {y^{\prime \prime }-8 y^{\prime }+15 y=9 \,{\mathrm e}^{2 x} x} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 10] \end {align*}
program solution	\[ y = \left (4+3 x \right ) {\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x}-2 \,{\mathrm e}^{5 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 \,{\mathrm e}^{5 x}+3 \,{\mathrm e}^{3 x}+\left (3 x +4\right ) {\mathrm e}^{2 x} \]