2.17.137 Problems 13601 to 13700

Problem 13601

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

Problem 13602

ODE	\[ \boxed {y^{\prime \prime }+25 y=0} \]
program solution	\[ y = c_{1} \cos \left (5 x \right )+\frac {c_{2} \sin \left (5 x \right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \sin \left (5 x \right )+c_{2} \cos \left (5 x \right ) \]

Problem 13603

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

Problem 13604

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

Problem 13605

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+29 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x} \cos \left (5 x \right )+\frac {c_{2} {\mathrm e}^{2 x} \sin \left (5 x \right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (c_{1} \sin \left (5 x \right )+c_{2} \cos \left (5 x \right )\right ) \]

Problem 13606

ODE	\[ \boxed {9 y^{\prime \prime }+18 y^{\prime }+10 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x} \cos \left (\frac {x}{3}\right )+3 c_{2} {\mathrm e}^{-x} \sin \left (\frac {x}{3}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{1} \sin \left (\frac {x}{3}\right )+c_{2} \cos \left (\frac {x}{3}\right )\right ) \]

Problem 13607

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 13608

ODE	\[ \boxed {y^{\prime \prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = \cos \left (4 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \cos \left (4 x \right ) \]

Problem 13609

ODE	\[ \boxed {y^{\prime \prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ y = \frac {\sin \left (4 x \right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sin \left (4 x \right )}{4} \]

Problem 13610

ODE	\[ \boxed {y^{\prime \prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 12] \end {align*}
program solution	\[ y = 4 \cos \left (4 x \right )+3 \sin \left (4 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]

Problem 13611

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

Problem 13612

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

Problem 13613

ODE	\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 31] \end {align*}
program solution	\[ y = {\mathrm e}^{2 x} \left (5 \cos \left (3 x \right )+7 \sin \left (3 x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (7 \sin \left (3 x \right )+5 \cos \left (3 x \right )\right ) \]

Problem 13614

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

Problem 13615

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

Problem 13616

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

Problem 13617

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

Problem 13618

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y=0} \]
program solution	\[ y = {\mathrm e}^{-3 x} c_{1} +c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{-5 x} c_{3} +{\mathrm e}^{5 x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left ({\mathrm e}^{10 x} c_{1} +c_{3} {\mathrm e}^{8 x}+c_{2} {\mathrm e}^{2 x}+c_{4} \right ) {\mathrm e}^{-5 x} \]

Problem 13619

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

Problem 13620

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

Problem 13621

ODE	\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=0} \]
program solution	\[ y = c_{1} +{\mathrm e}^{-3 i x} c_{2} +x \,{\mathrm e}^{-3 i x} c_{3} +{\mathrm e}^{3 i x} c_{4} +x \,{\mathrm e}^{3 i x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{5} x +c_{3} \right ) \cos \left (3 x \right )+\left (c_{4} x +c_{2} \right ) \sin \left (3 x \right )+c_{1} \]

Problem 13622

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{i x} c_{2} +{\mathrm e}^{-i x} c_{3} \] 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 13623

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{3 x}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{2 x} \]

Problem 13624

ODE	\[ \boxed {y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{\left (3-4 i\right ) x} c_{2} +{\mathrm e}^{\left (3+4 i\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{3 x} \sin \left (4 x \right )+c_{3} {\mathrm e}^{3 x} \cos \left (4 x \right ) \]

Problem 13625

ODE	\[ \boxed {y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y=0} \]
program solution	\[ y = {\mathrm e}^{\left (3+2 i\right ) x} c_{1} +c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{\left (3-2 i\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{1} +c_{2} \sin \left (2 x \right )+c_{3} \cos \left (2 x \right )\right ) \]

Problem 13626

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

Problem 13627

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y=0} \]
program solution	\[ y = {\mathrm e}^{-x} c_{1} +x \,{\mathrm e}^{-x} c_{2} +{\mathrm e}^{-3 i x} c_{3} +{\mathrm e}^{3 i x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{2} x +c_{1} \right )+c_{3} \sin \left (3 x \right )+c_{4} \cos \left (3 x \right ) \]

Problem 13628

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

Problem 13629

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 13, y^{\prime \prime }\left (0\right ) = 86] \end {align*}
program solution	\[ y = {\mathrm e}^{2 x} \left (27 x^{2}+3 x +5\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (27 x^{2}+3 x +5\right ) \]

Problem 13630

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = -28, y^{\prime \prime }\left (0\right ) = -102, y^{\prime \prime \prime }\left (0\right ) = 622] \end {align*}
program solution	\[ y = 4 \cos \left (5 x \right )-\frac {99 \sin \left (5 x \right )}{20}+2 \cos \left (x \right )-\frac {13 \sin \left (x \right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {13 \sin \left (x \right )}{4}+2 \cos \left (x \right )-\frac {99 \sin \left (5 x \right )}{20}+4 \cos \left (5 x \right ) \]

Problem 13631

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 10, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 6, y^{\prime \prime \prime }\left (0\right ) = -60] \end {align*}
program solution	\[ y = 6 \,{\mathrm e}^{-x}+4+2 \sin \left (3 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 4+6 \,{\mathrm e}^{-x}+2 \sin \left (3 x \right ) \]

Problem 13632

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

Problem 13633

ODE	\[ \boxed {y^{\prime \prime \prime }+216 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-6 x}+{\mathrm e}^{\left (3+3 i \sqrt {3}\right ) x} c_{2} +{\mathrm e}^{\left (3-3 i \sqrt {3}\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{9 x} \sin \left (3 \sqrt {3}\, x \right )+c_{3} {\mathrm e}^{9 x} \cos \left (3 \sqrt {3}\, x \right )+c_{1} \right ) {\mathrm e}^{-6 x} \]

Problem 13634

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

Problem 13635

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y=0} \]
program solution	\[ y = {\mathrm e}^{-2 i x} c_{1} +{\mathrm e}^{-3 i x} c_{2} +{\mathrm e}^{2 i x} c_{3} +{\mathrm e}^{3 i x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )+c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]

Problem 13636

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

Problem 13637

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

Problem 13638

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

Problem 13639

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

Problem 13640

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

Problem 13641

ODE	\[ \boxed {y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+x \,{\mathrm e}^{-2 x} c_{2} +{\mathrm e}^{\left (1+i \sqrt {3}\right ) x} c_{3} +x \,{\mathrm e}^{\left (1+i \sqrt {3}\right ) x} c_{4} +{\mathrm e}^{\left (1-i \sqrt {3}\right ) x} c_{5} +x \,{\mathrm e}^{\left (1-i \sqrt {3}\right ) x} c_{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left ({\mathrm e}^{3 x} \left (c_{6} x +c_{4} \right ) \cos \left (\sqrt {3}\, x \right )+{\mathrm e}^{3 x} \left (c_{5} x +c_{3} \right ) \sin \left (\sqrt {3}\, x \right )+c_{2} x +c_{1} \right ) {\mathrm e}^{-2 x} \]

Problem 13642

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

Problem 13643

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

Problem 13644

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

Problem 13645

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

Problem 13646

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

Problem 13647

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

Problem 13648

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

Problem 13649

ODE	\[ \boxed {x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y=0} \]
program solution	\[ y = c_{1} x^{10}+c_{2} x^{10} \ln \left (x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{10} \left (c_{1} +c_{2} \ln \left (x \right )\right ) \]

Problem 13650

ODE	\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y=0} \]
program solution	\[ y = c_{1} x^{3-2 i \sqrt {5}}-\frac {i c_{2} \sqrt {5}\, x^{3+2 i \sqrt {5}}}{20} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{3} \left (c_{1} \sin \left (2 \sqrt {5}\, \ln \left (x \right )\right )+c_{2} \cos \left (2 \sqrt {5}\, \ln \left (x \right )\right )\right ) \]

Problem 13651

ODE	\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +10 y=0} \]
program solution	\[ y = x^{1-3 i} c_{1} -\frac {i c_{2} x^{1+3 i}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]

Problem 13652

ODE	\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y=0} \]
program solution	\[ y = c_{1} x^{-2-5 i}-\frac {i c_{2} x^{-2+5 i}}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1} \sin \left (5 \ln \left (x \right )\right )+c_{2} \cos \left (5 \ln \left (x \right )\right )}{x^{2}} \]

Problem 13653

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

Problem 13654

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

Problem 13655

ODE	\[ \boxed {4 x^{2} y^{\prime \prime }+37 y=0} \]
program solution	\[ y = c_{1} x^{\frac {1}{2}-3 i}-\frac {i c_{2} x^{\frac {1}{2}+3 i}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x}\, \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]

Problem 13656

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

Problem 13657

ODE	\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -25 y=0} \]
program solution	\[ y = \frac {c_{1}}{x^{5}}+\frac {c_{2} x^{5}}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{5} c_{1} +\frac {c_{2}}{x^{5}} \]

Problem 13658

ODE	\[ \boxed {4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y=0} \]
program solution	\[ y = c_{1} x^{-\frac {1}{2}-i}-\frac {i c_{2} x^{-\frac {1}{2}+i}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1} \sin \left (\ln \left (x \right )\right )+c_{2} \cos \left (\ln \left (x \right )\right )}{\sqrt {x}} \]

Problem 13659

ODE	\[ \boxed {3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y=0} \]
program solution	\[ y = x^{\frac {1}{3}} c_{1} +\frac {3 x^{3} c_{2}}{8} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}}+c_{2} x^{3} \]

Problem 13660

ODE	\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 5, y^{\prime }\left (1\right ) = 4] \end {align*}
program solution	\[ y = \frac {2 x^{7}+3}{x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 x^{5}+\frac {3}{x^{2}} \]

Problem 13661

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

Problem 13662

ODE	\[ \boxed {x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}, y^{\prime }\left (1\right ) = 2\right ] \end {align*}
program solution	\[ y = \left (-\ln \left (x \right )+\frac {1}{2}\right ) x^{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{6} \left (\frac {1}{2}-\ln \left (x \right )\right ) \]

Problem 13663

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

Problem 13664

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

Problem 13665

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

Problem 13666

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

Problem 13667

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

Problem 13668

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y=0} \]
program solution	\[ y = x^{3} c_{2} +c_{1} x^{2}+c_{3} \ln \left (x \right ) x^{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{2} \left (\ln \left (x \right ) c_{3} x +c_{2} x +c_{1} \right ) \]

Problem 13669

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y=0} \]
program solution	\[ y = c_{1} x^{2}+c_{2} \ln \left (x \right ) x^{2}+c_{3} \ln \left (x \right )^{2} x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{2} \left (c_{1} +c_{2} \ln \left (x \right )+c_{3} \ln \left (x \right )^{2}\right ) \]

Problem 13670

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y=0} \]
program solution	\[ y = c_{1} \cos \left (2 \ln \left (x \right )\right )+c_{2} \sin \left (2 \ln \left (x \right )\right )+\ln \left (x \right ) \left (c_{3} \cos \left (2 \ln \left (x \right )\right )+c_{4} \sin \left (2 \ln \left (x \right )\right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{4} \ln \left (x \right )+c_{2} \right ) \cos \left (2 \ln \left (x \right )\right )+\sin \left (2 \ln \left (x \right )\right ) \left (c_{3} \ln \left (x \right )+c_{1} \right ) \]

Problem 13671

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

Problem 13672

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

Problem 13673

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

Problem 13674

ODE	\[ \boxed {y^{\prime \prime }+4 y=24 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 6] \end {align*}
program solution	\[ y = 3 \,{\mathrm e}^{2 x}+3 \cos \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \cos \left (2 x \right )+3 \,{\mathrm e}^{2 x} \]

Problem 13675

ODE	\[ \boxed {y^{\prime \prime }+4 y=24 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 2] \end {align*}
program solution	\[ y = 3 \,{\mathrm e}^{2 x}-5 \cos \left (2 x \right )-2 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 \sin \left (2 x \right )-5 \cos \left (2 x \right )+3 \,{\mathrm e}^{2 x} \]

Problem 13676

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

Problem 13677

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

Problem 13678

ODE	\[ \boxed {y^{\prime \prime }-9 y=36} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = 6] \end {align*}
program solution	\[ y = -4+7 \,{\mathrm e}^{3 x}+5 \,{\mathrm e}^{-3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 5 \,{\mathrm e}^{-3 x}+7 \,{\mathrm e}^{3 x}-4 \]

Problem 13679

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

Problem 13680

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=7 \,{\mathrm e}^{5 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 12, y^{\prime }\left (0\right ) = -2] \end {align*}
program solution	\[ y = \left (9+{\mathrm e}^{7 x} \left (3+x \right )\right ) {\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (9+\left (x +3\right ) {\mathrm e}^{7 x}\right ) {\mathrm e}^{-2 x} \]

Problem 13681

ODE	\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=169 \sin \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -10, y^{\prime }\left (0\right ) = 9] \end {align*}
program solution	\[ y = \left (5 x +2\right ) {\mathrm e}^{-3 x}-12 \cos \left (2 x \right )+5 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (5 x +2\right ) {\mathrm e}^{-3 x}-12 \cos \left (2 x \right )+5 \sin \left (2 x \right ) \]

Problem 13682

ODE	\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=10 x +12} \] With initial conditions \begin {align*} [y \left (1\right ) = 6, y^{\prime }\left (1\right ) = 8] \end {align*}
program solution	\[ y = 5 x^{3}-6 x^{2}+5 x +2 \] Verified OK.
Maple solution	\[ y \left (x \right ) = 5 x^{3}-6 x^{2}+5 x +2 \]

Problem 13683

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

Problem 13684

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

Problem 13685

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y={\mathrm e}^{5 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}+\frac {{\mathrm e}^{5 x} \left (7 x -1\right )}{49} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x} \left (\left (x +7 c_{2} \right ) {\mathrm e}^{7 x}+7 c_{1} \right )}{7} \]

Problem 13686

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}+3 \,{\mathrm e}^{4 x}-\frac {2 \,{\mathrm e}^{5 x}}{7}+2 \,{\mathrm e}^{5 x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (14 x +7 c_{2} -2\right ) {\mathrm e}^{7 x}}{7}+c_{1} +3 \,{\mathrm e}^{6 x}\right ) \]

Problem 13687

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{5 x}}{7}-2 \,{\mathrm e}^{4 x}-\frac {5 \,{\mathrm e}^{5 x}}{7}+5 \,{\mathrm e}^{5 x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (35 x +7 c_{2} -5\right ) {\mathrm e}^{7 x}}{7}+c_{1} -2 \,{\mathrm e}^{6 x}\right ) \]

Problem 13688

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

Problem 13689

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

Problem 13690

ODE	\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=22 x +24} \]
program solution	\[ y = x^{2} \left (c_{2} x +c_{1} \right )+4+11 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{3}+c_{1} x^{2}+11 x +4 \]

Problem 13691

ODE	\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y=x^{2}} \]
program solution	\[ y = c_{1} x^{3}+\frac {1}{2} c_{2} x^{5}+\frac {1}{3} x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{3} x^{2} \]

Problem 13692

ODE	\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y=x} \]
program solution	\[ y = c_{1} x^{3}+\frac {1}{2} c_{2} x^{5}+\frac {1}{8} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{8} x \]

Problem 13693

ODE	\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y=1} \]
program solution	\[ y = c_{1} x^{3}+\frac {1}{2} c_{2} x^{5}+\frac {1}{15} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{15} \]

Problem 13694

ODE	\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y=4 x^{2}+2 x +3} \]
program solution	\[ y = c_{1} x^{3}+\frac {1}{2} c_{2} x^{5}+\frac {1}{5}+\frac {1}{4} x +\frac {4}{3} x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{5}+\frac {4}{3} x^{2}+\frac {1}{4} x \]

Problem 13695

ODE	\[ \boxed {y^{\prime \prime }+9 y=52 \,{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+4 \,{\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+4 \,{\mathrm e}^{2 x} \]

Problem 13696

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

Problem 13697

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=30 \,{\mathrm e}^{-4 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-5 x}+\frac {c_{2} {\mathrm e}^{x}}{6}-6 \,{\mathrm e}^{-4 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left ({\mathrm e}^{6 x} c_{2} -6 \,{\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-5 x} \]

Problem 13698

ODE	\[ \boxed {y^{\prime \prime }+3 y^{\prime }={\mathrm e}^{\frac {x}{2}}} \]
program solution	\[ y = \frac {\left (12 \,{\mathrm e}^{\frac {7 x}{2}}+7 c_{1} {\mathrm e}^{3 x}+21 c_{2} \right ) {\mathrm e}^{-3 x}}{21} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} \left (-3 c_{2} {\mathrm e}^{3 x}+c_{1} -\frac {12 \,{\mathrm e}^{\frac {7 x}{2}}}{7}\right )}{3} \]

Problem 13699

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

Problem 13700

ODE	\[ \boxed {y^{\prime \prime }+9 y=10 \cos \left (2 x \right )+15 \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+2 \cos \left (2 x \right )+3 \sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+3 \sin \left (2 x \right )+2 \cos \left (2 x \right ) \]