2.17.138 Problems 13701 to 13800

Problem 13701

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=25 \sin \left (6 x \right )} \]
program solution	\[ y = {\mathrm e}^{3 x} \left (c_{2} x +c_{1} \right )+\frac {4 \cos \left (6 x \right )}{9}-\frac {\sin \left (6 x \right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {4 \cos \left (6 x \right )}{9}-\frac {\sin \left (6 x \right )}{3} \]

Problem 13702

ODE	\[ \boxed {y^{\prime \prime }+3 y^{\prime }=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )} \]
program solution	\[ y = \frac {c_{1}}{3}+27 \sin \left (\frac {x}{3}\right )+9 \cos \left (\frac {x}{3}\right )+c_{2} {\mathrm e}^{-3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {c_{1} {\mathrm e}^{-3 x}}{3}+27 \sin \left (\frac {x}{3}\right )+9 \cos \left (\frac {x}{3}\right )+c_{2} \]

Problem 13703

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=\cos \left (x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{x}}{6}-\frac {3 \cos \left (x \right )}{26}+\frac {\sin \left (x \right )}{13} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\frac {\left (-3 \cos \left (x \right )+2 \sin \left (x \right )\right ) {\mathrm e}^{5 x}}{26}+c_{1} +{\mathrm e}^{6 x} c_{2} \right ) {\mathrm e}^{-5 x} \]

Problem 13704

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-4 \cos \left (x \right )+7 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = -5] \end {align*}
program solution	\[ y = \frac {3 \,{\mathrm e}^{5 x}}{2}+6 \,{\mathrm e}^{-2 x}-\frac {\sin \left (x \right )}{2}+\frac {\cos \left (x \right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x} \left (\left (\cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{2 x}+3 \,{\mathrm e}^{7 x}+12\right )}{2} \]

Problem 13705

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-200} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}+20 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{7 x}+20 \,{\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]

Problem 13706

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=x^{3}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{x}}{6}-\frac {x^{3}}{5}-\frac {12 x^{2}}{25}-\frac {126 x}{125}-\frac {624}{625} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-5 x} \left (\left (x^{3}+\frac {12}{5} x^{2}+\frac {126}{25} x +\frac {624}{125}\right ) {\mathrm e}^{5 x}-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{1} \right )}{5} \]

Problem 13707

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

Problem 13708

ODE	\[ \boxed {y^{\prime \prime }+9 y=9 x^{4}-9} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+x^{4}-\frac {4 x^{2}}{3}-\frac {19}{27} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+x^{4}-\frac {4 x^{2}}{3}-\frac {19}{27} \]

Problem 13709

ODE	\[ \boxed {y^{\prime \prime }+9 y=x^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {2 \sin \left (3 x \right )}{81}+\frac {x^{3}}{9}-\frac {2 x}{27} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 \sin \left (3 x \right )}{81}+\frac {x^{3}}{9}-\frac {2 x}{27} \]

Problem 13710

ODE	\[ \boxed {y^{\prime \prime }+9 y=25 x \cos \left (2 x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+5 x \cos \left (2 x \right )+4 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+5 \cos \left (2 x \right ) x +4 \sin \left (2 x \right ) \]

Problem 13711

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

Problem 13712

ODE	\[ \boxed {y^{\prime \prime }+9 y=54 x^{2} {\mathrm e}^{3 x}} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+3 x^{2} {\mathrm e}^{3 x}-2 \,{\mathrm e}^{3 x} x +\frac {{\mathrm e}^{3 x}}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+3 \left (x -\frac {1}{3}\right )^{2} {\mathrm e}^{3 x} \]

Problem 13713

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

Problem 13714

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

Problem 13715

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

Problem 13716

ODE	\[ \boxed {y^{\prime \prime }+9 y=39 x \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {25 \cos \left (3 x \right )}{13}-\frac {5 \sin \left (3 x \right )}{13}+3 x \,{\mathrm e}^{2 x}-\frac {12 \,{\mathrm e}^{2 x}}{13} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 x \,{\mathrm e}^{2 x}+\frac {25 \cos \left (3 x \right )}{13}-\frac {5 \sin \left (3 x \right )}{13}-\frac {12 \,{\mathrm e}^{2 x}}{13} \]

Problem 13717

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

Problem 13718

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

Problem 13719

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }=x^{2}} \]
program solution	\[ y = \frac {x^{3}}{12}-\frac {x^{2}}{16}+\frac {c_{1}}{4}+\frac {x}{32}-\frac {1}{128}+c_{2} {\mathrm e}^{-4 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{2}}{16}+\frac {x^{3}}{12}-\frac {{\mathrm e}^{-4 x} c_{1}}{4}+\frac {x}{32}+c_{2} \]

Problem 13720

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

Problem 13721

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=10 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = {\mathrm e}^{3 x} \left (c_{2} x +c_{1} \right )+5 x^{2} {\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{1} x +5 x^{2}+c_{2} \right ) \]

Problem 13722

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}-x \,{\mathrm e}^{2 x}-6 x^{2} {\mathrm e}^{2 x}-{\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (-6 x^{2}-x -1\right ) {\mathrm e}^{-2 x} {\mathrm e}^{4 x}+\left (c_{2} {\mathrm e}^{7 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]

Problem 13723

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=4 x \,{\mathrm e}^{6 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}+\frac {x \,{\mathrm e}^{6 x}}{2}-\frac {9 \,{\mathrm e}^{6 x}}{16} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (8 \,{\mathrm e}^{8 x} x -9 \,{\mathrm e}^{8 x}+16 c_{2} {\mathrm e}^{7 x}+16 c_{1} \right ) {\mathrm e}^{-2 x}}{16} \]

Problem 13724

ODE	\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=6 \,{\mathrm e}^{5 x}} \]
program solution	\[ y = {\mathrm e}^{5 x} \left (c_{2} x +c_{1} \right )+3 x^{2} {\mathrm e}^{5 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{5 x} \left (c_{1} x +3 x^{2}+c_{2} \right ) \]

Problem 13725

ODE	\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=6 \,{\mathrm e}^{-5 x}} \]
program solution	\[ y = {\mathrm e}^{5 x} \left (c_{2} x +c_{1} \right )+\frac {3 \,{\mathrm e}^{-5 x}}{50} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{5 x}+\frac {3 \,{\mathrm e}^{-5 x}}{50} \]

Problem 13726

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=24 \sin \left (3 x \right )} \]
program solution	\[ y = {\mathrm e}^{-2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )-\frac {9 \cos \left (3 x \right )}{5}-\frac {3 \sin \left (3 x \right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} -\frac {3 \sin \left (3 x \right )}{5}-\frac {9 \cos \left (3 x \right )}{5} \]

Problem 13727

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

Problem 13728

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

Problem 13729

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y={\mathrm e}^{-x} \sin \left (x \right )} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )+\frac {2 \,{\mathrm e}^{-x} \cos \left (x \right )}{39}+\frac {{\mathrm e}^{-x} \sin \left (x \right )}{13} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \left (2 \cos \left (x \right )+3 \sin \left (x \right )\right )}{39}+\left (\sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )\right ) {\mathrm e}^{2 x} \]

Problem 13730

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=100} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )+20 \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +20 \]

Problem 13731

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

Problem 13732

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=10 x^{2}+4 x +8} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )+2 x^{2}+4 x +4 \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +2 x^{2}+4 x +4 \]

Problem 13733

ODE	\[ \boxed {y^{\prime \prime }+9 y={\mathrm e}^{2 x} \sin \left (x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}-\frac {{\mathrm e}^{2 x} \cos \left (x \right )}{40}+\frac {3 \,{\mathrm e}^{2 x} \sin \left (x \right )}{40} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (3 \sin \left (x \right )-\cos \left (x \right )\right )}{40}+c_{1} \cos \left (3 x \right )+c_{2} \sin \left (3 x \right ) \]

Problem 13734

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

Problem 13735

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

Problem 13736

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=x^{3} {\mathrm e}^{-x} \sin \left (x \right )} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )+\frac {38200 \,{\mathrm e}^{-x} \cos \left (x \right )}{771147}+\frac {360 \,{\mathrm e}^{-x} \sin \left (x \right )}{28561}+\frac {138 x \,{\mathrm e}^{-x} \sin \left (x \right )}{2197}+\frac {2 x^{3} {\mathrm e}^{-x} \cos \left (x \right )}{39}+\frac {x^{3} {\mathrm e}^{-x} \sin \left (x \right )}{13}+\frac {2440 \,{\mathrm e}^{-x} \cos \left (x \right ) x}{19773}+\frac {62 \,{\mathrm e}^{-x} \cos \left (x \right ) x^{2}}{507}+\frac {18 \,{\mathrm e}^{-x} \sin \left (x \right ) x^{2}}{169} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (39546 x^{3}+94302 x^{2}+95160 x +38200\right ) \cos \left (x \right )+59319 \left (x^{3}+\frac {18}{13} x^{2}+\frac {138}{169} x +\frac {360}{2197}\right ) \sin \left (x \right )\right ) {\mathrm e}^{-x}}{771147}+\left (\sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )\right ) {\mathrm e}^{2 x} \]

Problem 13737

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

Problem 13738

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x}+\frac {19 x \,{\mathrm e}^{-7 x}}{4050}+\frac {x^{2} {\mathrm e}^{-7 x}}{90}+\frac {8371 \,{\mathrm e}^{-7 x}}{364500} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-7 x} \left (x^{2}+90 \,{\mathrm e}^{9 x} c_{1} +90 c_{2} {\mathrm e}^{10 x}+\frac {19 x}{45}+\frac {8371}{4050}\right )}{90} \]

Problem 13739

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x}+\frac {x^{2}}{6}+\frac {5 x}{18}+\frac {19}{108} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{2 x} c_{1} +\frac {x^{2}}{6}+\frac {5 x}{18}+\frac {19}{108} \]

Problem 13740

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=4 \,{\mathrm e}^{-8 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x}+\frac {2 \,{\mathrm e}^{-8 x}}{55} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-8 x} \left ({\mathrm e}^{10 x} c_{1} +c_{2} {\mathrm e}^{11 x}+\frac {2}{55}\right ) \]

Problem 13741

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

Problem 13742

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

Problem 13743

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} \cos \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x}-\frac {10 x \cos \left (2 x \right )}{169}-\frac {73 x \sin \left (2 x \right )}{676}+\frac {x^{2} \cos \left (2 x \right )}{52}-\frac {5 x^{2} \sin \left (2 x \right )}{52}-\frac {1909 \cos \left (2 x \right )}{35152}-\frac {725 \sin \left (2 x \right )}{35152} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{2 x} c_{1} +\frac {\left (676 x^{2}-2080 x -1909\right ) \cos \left (2 x \right )}{35152}+\frac {\left (-3380 x^{2}-3796 x -725\right ) \sin \left (2 x \right )}{35152} \]

Problem 13744

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x}+\frac {109 \,{\mathrm e}^{3 x} \cos \left (2 x \right )}{500}+\frac {22 \,{\mathrm e}^{3 x} \sin \left (2 x \right )}{125}-\frac {8 x \cos \left (2 x \right ) {\mathrm e}^{3 x}}{25}+\frac {13 x \sin \left (2 x \right ) {\mathrm e}^{3 x}}{50}-\frac {x^{2} \cos \left (2 x \right ) {\mathrm e}^{3 x}}{10}-\frac {x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-50 x^{2}-160 x +109\right ) \cos \left (2 x \right )+\left (-100 x^{2}+130 x +88\right ) \sin \left (2 x \right )+500 c_{2} \right ) {\mathrm e}^{3 x}}{500}+{\mathrm e}^{2 x} c_{1} \]

Problem 13745

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

Problem 13746

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

Problem 13747

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+20 y=x^{3} \sin \left (4 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x} \cos \left (4 x \right )+\frac {c_{2} {\mathrm e}^{2 x} \sin \left (4 x \right )}{4}-\frac {39 x \sin \left (4 x \right )}{39304}+\frac {57 x^{2} \cos \left (4 x \right )}{578}+\frac {3 x^{2} \sin \left (4 x \right )}{1156}+\frac {x^{3} \cos \left (4 x \right )}{17}+\frac {x^{3} \sin \left (4 x \right )}{68}+\frac {465 \cos \left (4 x \right ) x}{4913}+\frac {7815 \cos \left (4 x \right )}{167042}-\frac {45 \sin \left (4 x \right )}{334084} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (9826 x^{3}+16473 x^{2}+167042 \,{\mathrm e}^{2 x} c_{1} +15810 x +7815\right ) \cos \left (4 x \right )}{167042}+\frac {\left (x^{3}+\frac {3 x^{2}}{17}+68 c_{2} {\mathrm e}^{2 x}-\frac {39 x}{578}-\frac {45}{4913}\right ) \sin \left (4 x \right )}{68} \]

Problem 13748

ODE	\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=3 x^{2} {\mathrm e}^{5 x}} \]
program solution	\[ y = {\mathrm e}^{5 x} \left (c_{2} x +c_{1} \right )+\frac {x^{4} {\mathrm e}^{5 x}}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{5 x} \left (c_{2} +c_{1} x +\frac {1}{4} x^{4}\right ) \]

Problem 13749

ODE	\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=3 x^{4}} \]
program solution	\[ y = {\mathrm e}^{5 x} \left (c_{2} x +c_{1} \right )+\frac {3 x^{4}}{25}+\frac {24 x^{3}}{125}+\frac {108 x^{2}}{625}+\frac {288 x}{3125}+\frac {72}{3125} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {72}{3125}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{5 x}+\frac {3 x^{4}}{25}+\frac {24 x^{3}}{125}+\frac {108 x^{2}}{625}+\frac {288 x}{3125} \]

Problem 13750

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=12 \,{\mathrm e}^{-2 x}} \]
program solution	\[ y = x^{2} c_{3} +c_{2} x +c_{1} +{\mathrm e}^{4 x} c_{4} +\frac {{\mathrm e}^{-2 x}}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+\frac {{\mathrm e}^{-2 x}}{4}+c_{3} x +c_{4} \]

Problem 13751

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=10 \sin \left (2 x \right )} \]
program solution	\[ y = x^{2} c_{3} +c_{2} x +c_{1} +{\mathrm e}^{4 x} c_{4} -\frac {\cos \left (2 x \right )}{4}+\frac {\sin \left (2 x \right )}{8} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+\frac {\sin \left (2 x \right )}{8}-\frac {\cos \left (2 x \right )}{4}+c_{3} x +c_{4} \]

Problem 13752

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=32 \,{\mathrm e}^{4 x}} \]
program solution	\[ y = x^{2} c_{3} +c_{2} x +c_{1} +{\mathrm e}^{4 x} c_{4} +\frac {x \,{\mathrm e}^{4 x}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (32 x +c_{1} -24\right ) {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_{4} \]

Problem 13753

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=32 x} \]
program solution	\[ y = x^{2} c_{3} +c_{2} x +c_{1} +{\mathrm e}^{4 x} c_{4} -\frac {x^{4}}{3}-\frac {x^{3}}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x^{4}}{3}-\frac {x^{3}}{3}+\frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_{4} \]

Problem 13754

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

Problem 13755

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

Problem 13756

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

Problem 13757

ODE	\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=x^{2} {\mathrm e}^{3 x}} \]
program solution	\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{-3 i x}+\left (c_{5} x +c_{4} \right ) {\mathrm e}^{3 i x}+c_{1} +\frac {x^{2} {\mathrm e}^{3 x}}{972}-\frac {{\mathrm e}^{3 x} x}{486}+\frac {5 \,{\mathrm e}^{3 x}}{4374} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-3 c_{4} x -3 c_{2} +c_{3} \right ) \cos \left (3 x \right )}{9}+\frac {\left (9 x^{2}-18 x +10\right ) {\mathrm e}^{3 x}}{8748}+\frac {\left (3 c_{3} x +3 c_{1} +c_{4} \right ) \sin \left (3 x \right )}{9}+c_{5} \]

Problem 13758

ODE	\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=x^{2} \sin \left (3 x \right )} \]
program solution	\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{-3 i x}+\left (c_{5} x +c_{4} \right ) {\mathrm e}^{3 i x}+c_{1} +\frac {\left (18 x^{4}-66 x^{2}+19\right ) \cos \left (3 x \right )}{23328}+\frac {\left (-12 x^{3}+13 x \right ) \sin \left (3 x \right )}{5832} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (18 x^{4}-7776 c_{4} x -66 x^{2}-7776 c_{2} +2592 c_{3} +19\right ) \cos \left (3 x \right )}{23328}+\frac {\left (-12 x^{3}+\left (13+1944 c_{3} \right ) x +1944 c_{1} +648 c_{4} \right ) \sin \left (3 x \right )}{5832}+c_{5} \]

Problem 13759

ODE	\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=\sin \left (3 x \right ) x^{2} {\mathrm e}^{3 x}} \]
program solution	\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{-3 i x}+\left (c_{5} x +c_{4} \right ) {\mathrm e}^{3 i x}+c_{1} +\frac {139 \cos \left (3 x \right ) {\mathrm e}^{3 x}}{303750}-\frac {1693 \sin \left (3 x \right ) {\mathrm e}^{3 x}}{2733750}-\frac {31 x \cos \left (3 x \right ) {\mathrm e}^{3 x}}{91125}+\frac {4 x \sin \left (3 x \right ) {\mathrm e}^{3 x}}{3375}-\frac {\cos \left (3 x \right ) x^{2} {\mathrm e}^{3 x}}{12150}-\frac {7 \sin \left (3 x \right ) x^{2} {\mathrm e}^{3 x}}{12150} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-75 x^{2}-310 x +417\right ) {\mathrm e}^{3 x}-303750 c_{4} x -303750 c_{2} +101250 c_{3} \right ) \cos \left (3 x \right )}{911250}+\frac {\left (-1575 x^{2}+3240 x -1693\right ) \sin \left (3 x \right ) {\mathrm e}^{3 x}}{2733750}+\frac {\left (3 c_{3} x +3 c_{1} +c_{4} \right ) \sin \left (3 x \right )}{9}+c_{5} \]

Problem 13760

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=30 x \cos \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{i x} c_{2} +{\mathrm e}^{-i x} c_{3} +2 x \cos \left (2 x \right )-4 x \sin \left (2 x \right )-\frac {98 \cos \left (2 x \right )}{15}-\frac {64 \sin \left (2 x \right )}{15} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (30 x -98\right ) \cos \left (2 x \right )}{15}+\frac {\left (-60 x -64\right ) \sin \left (2 x \right )}{15}+c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]

Problem 13761

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=3 \cos \left (x \right ) x} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{i x} c_{2} +{\mathrm e}^{-i x} c_{3} +\frac {3 \left (-4 x^{2}-12 x +i-3\right ) \cos \left (x \right )}{32}+\frac {3 \sin \left (x \right ) \left (-4 x^{2}+4 x -i+9\right )}{32} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-3 x^{2}+8 c_{3} +3 x +9\right ) \sin \left (x \right )}{8}+\frac {\left (-3 x^{2}+8 c_{1} -9 x \right ) \cos \left (x \right )}{8}+c_{2} {\mathrm e}^{x} \]

Problem 13762

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=3 \,{\mathrm e}^{x} \cos \left (x \right ) x} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{i x} c_{2} +{\mathrm e}^{-i x} c_{3} +\frac {57 \,{\mathrm e}^{x} \cos \left (x \right )}{25}+\frac {24 \,{\mathrm e}^{x} \sin \left (x \right )}{25}-\frac {6 \,{\mathrm e}^{x} \cos \left (x \right ) x}{5}+\frac {3 \,{\mathrm e}^{x} \sin \left (x \right ) x}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-30 x +57\right ) \cos \left (x \right )+\left (15 x +24\right ) \sin \left (x \right )+25 c_{2} \right ) {\mathrm e}^{x}}{25}+c_{1} \cos \left (x \right )+c_{3} \sin \left (x \right ) \]

Problem 13763

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=5 x^{5} {\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{i x} c_{2} +{\mathrm e}^{-i x} c_{3} +\frac {37464 x \,{\mathrm e}^{2 x}}{125}-\frac {3648 x^{2} {\mathrm e}^{2 x}}{25}+\frac {224 x^{3} {\mathrm e}^{2 x}}{5}-9 x^{4} {\mathrm e}^{2 x}+x^{5} {\mathrm e}^{2 x}-\frac {188376 \,{\mathrm e}^{2 x}}{625} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (625 x^{5}-5625 x^{4}+28000 x^{3}-91200 x^{2}+187320 x -188376\right ) {\mathrm e}^{2 x}}{625}+c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]

Problem 13764

ODE	\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )} \]
program solution	\[ y = {\mathrm e}^{3 x} \left (c_{2} x +c_{1} \right )+3 \,{\mathrm e}^{6 x}+\frac {4 \cos \left (6 x \right )}{9}-\frac {\sin \left (6 x \right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {4 \cos \left (6 x \right )}{9}+3 \,{\mathrm e}^{6 x}-\frac {\sin \left (6 x \right )}{3} \]

Problem 13765

ODE	\[ \boxed {y^{\prime \prime }+9 y=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}-\frac {\cos \left (3 x \right ) x}{2}+5 x \cos \left (2 x \right )+4 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 c_{1} -x \right ) \cos \left (3 x \right )}{2}+\frac {\left (1+12 c_{2} \right ) \sin \left (3 x \right )}{12}+5 \cos \left (2 x \right ) x +4 \sin \left (2 x \right ) \]

Problem 13766

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=5 \sin \left (x \right )^{2}} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )\right )+\frac {1}{2}-\frac {\cos \left (2 x \right )}{26}+\frac {4 \sin \left (2 x \right )}{13} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} -\frac {\cos \left (2 x \right )}{26}+\frac {1}{2}+\frac {4 \sin \left (2 x \right )}{13} \]

Problem 13767

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

Problem 13768

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

Problem 13769

ODE	\[ \boxed {2 x^{2} y^{\prime \prime }-y^{\prime } x +y=\frac {50}{x^{3}}} \]
program solution	\[ y = c_{1} \sqrt {x}+2 c_{2} x +\frac {25}{14 x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {14 c_{2} x^{\frac {7}{2}}+14 x^{4} c_{1} +25}{14 x^{3}} \]

Problem 13770

ODE	\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=85 \cos \left (2 \ln \left (x \right )\right )} \]
program solution	\[ y = \frac {\int \frac {17 \cos \left (2 \ln \left (x \right )\right ) x +34 x \sin \left (2 \ln \left (x \right )\right )+c_{1}}{x^{\frac {3}{2}}}d x +2 c_{2}}{2 \sqrt {x}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 c_{2} +\int \frac {c_{1} +17 \cos \left (2 \ln \left (x \right )\right ) x +34 x \sin \left (2 \ln \left (x \right )\right )}{x^{\frac {3}{2}}}d x}{2 \sqrt {x}} \]

Problem 13771

ODE	\[ \boxed {x^{2} y^{\prime \prime }-2 y=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )} \]
program solution	\[ y = \frac {\frac {\left (-3 \cos \left (3 \ln \left (x \right )\right )+\sin \left (3 \ln \left (x \right )\right )\right ) x}{2}-\frac {c_{1}}{3}+c_{2} x^{3}}{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} x^{2}-\frac {3 \cos \left (3 \ln \left (x \right )\right )}{2}+\frac {\sin \left (3 \ln \left (x \right )\right )}{2} \]

Problem 13772

ODE	\[ \boxed {3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y=4 x^{3}} \]
program solution	\[ y = x^{\frac {1}{3}} c_{1} +\frac {3 c_{2} x^{3}}{8}+\frac {x^{3} \left (-3+8 \ln \left (x \right )\right )}{16} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}}+\left (c_{2} +\frac {\ln \left (x \right )}{2}-\frac {3}{16}\right ) x^{3} \]

Problem 13773

ODE	\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=\frac {10}{x}} \]
program solution	\[ y = \frac {\sqrt {x}\, c_{2} -10 \ln \left (x \right )-c_{1} -20}{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-10 \sqrt {x}\, \ln \left (x \right )+c_{2} x +\left (c_{1} -20\right ) \sqrt {x}}{x^{\frac {3}{2}}} \]

Problem 13774

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

Problem 13775

ODE	\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=64 \ln \left (x \right ) x^{2}} \]
program solution	\[ y = \frac {c_{1} +c_{2} \ln \left (x \right )}{x^{2}}+2 x^{2} \left (-1+2 \ln \left (x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (4 x^{4}+c_{1} \right ) \ln \left (x \right )-2 x^{4}+c_{2}}{x^{2}} \]

Problem 13776

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

Problem 13777

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

Problem 13778

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

Problem 13779

ODE	\[ \boxed {y^{\prime \prime }-7 y^{\prime }+10 y=6 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{3}-3 \,{\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{5 x} c_{2} +{\mathrm e}^{2 x} c_{1} -3 \,{\mathrm e}^{3 x} \]

Problem 13780

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x}} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right )+x^{2} {\mathrm e}^{2 x}+2 x^{4} {\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (2 x^{4}+c_{1} x +x^{2}+c_{2} \right ) \]

Problem 13781

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

Problem 13782

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

Problem 13783

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

Problem 13784

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

Problem 13785

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

Problem 13786

ODE	\[ \boxed {x^{2} y^{\prime \prime }-2 y=\frac {1}{x -2}} \]
program solution	\[ y = \frac {\left (x^{3}-8\right ) \ln \left (x -2\right )+24 c_{2} x^{3}-\ln \left (x \right ) x^{3}+2 x^{2}+2 x -8 c_{1}}{24 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{3}-8\right ) \ln \left (x -2\right )+24 c_{2} x^{3}-\ln \left (x \right ) x^{3}+2 x^{2}+2 x +24 c_{1}}{24 x} \]

Problem 13787

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

Problem 13788

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

Problem 13789

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

Problem 13790

ODE	\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y=\frac {10}{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = -15] \end {align*}
program solution	\[ y = \frac {-2 x^{5}-2 \ln \left (x \right )+5}{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-2 x^{5}-2 \ln \left (x \right )+5}{x} \]

Problem 13791

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=12 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 8] \end {align*}
program solution	\[ y = -3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x}-{\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (4 \,{\mathrm e}^{5 x}-3 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]

Problem 13792

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=30 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = c_{1} +{\mathrm e}^{-2 x} c_{2} +{\mathrm e}^{2 x} c_{3} +2 \,{\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (-4 \,{\mathrm e}^{5 x}-c_{2} {\mathrm e}^{4 x}-2 c_{3} {\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-2 x}}{2} \]

Problem 13793

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

Problem 13794

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

Problem 13795

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

Problem 13796

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-81 y=\sinh \left (x \right )} \]
program solution	\[ y = {\mathrm e}^{-3 x} c_{1} +c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{-3 i x} c_{3} +{\mathrm e}^{3 i x} c_{4} +\frac {\left (5-40 \cosh \left (x \right ) \sinh \left (x \right )^{3}+\left (-40 \cosh \left (x \right )^{2}+20\right ) \sinh \left (x \right )^{2}\right ) {\mathrm e}^{-3 x}}{4320}+\frac {\left (-5-40 \cosh \left (x \right ) \sinh \left (x \right )^{3}+\left (40 \cosh \left (x \right )^{2}-20\right ) \sinh \left (x \right )^{2}\right ) {\mathrm e}^{3 x}}{4320}-\frac {\sinh \left (x \right )}{180} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (160 c_{3} {\mathrm e}^{6 x}+160 c_{1} \cos \left (3 x \right ) {\mathrm e}^{3 x}+160 c_{4} \sin \left (3 x \right ) {\mathrm e}^{3 x}-{\mathrm e}^{4 x}+{\mathrm e}^{2 x}+160 c_{2} \right ) {\mathrm e}^{-3 x}}{160} \]

Problem 13797

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y=12 \sin \left (x^{2}\right ) x} \]
program solution	\[ y = \frac {c_{1}}{x}+c_{2} x +\frac {c_{3}}{x^{3}}+c_{4} x^{3}+\frac {\operatorname {Ci}\left (x^{2}\right ) x^{6}-x^{4} \sin \left (x^{2}\right )-3 \,\operatorname {Si}\left (x^{2}\right ) x^{4}-2 x^{2} \cos \left (x^{2}\right )-\sin \left (x^{2}\right )}{8 x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-2 x^{4}-2\right ) \sin \left (x^{2}\right )+16 c_{4} x^{6}+2 \,\operatorname {Ci}\left (x^{2}\right ) x^{6}+16 c_{2} x^{4}-6 \,\operatorname {Si}\left (x^{2}\right ) x^{4}+c_{1} x^{2}-4 x^{2} \cos \left (x^{2}\right )+16 c_{3}}{16 x^{3}} \]

Problem 13798

ODE	\[ \boxed {y^{\prime \prime }+36 y=0} \]
program solution	\[ y = c_{1} \cos \left (6 x \right )+\frac {c_{2} \sin \left (6 x \right )}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \sin \left (6 x \right )+c_{2} \cos \left (6 x \right ) \]

Problem 13799

ODE	\[ \boxed {y^{\prime \prime }-12 y^{\prime }+36 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{6 x}+c_{2} x \,{\mathrm e}^{6 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{6 x} \left (c_{2} x +c_{1} \right ) \]

Problem 13800

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