2.17.16 Problems 1501 to 1600

Problem 1501

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

Problem 1502

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x}+{\mathrm e}^{-3 x} c_{3} -\frac {x \,{\mathrm e}^{x}}{2}+\frac {x^{2} {\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{x} x^{3}}{2}+\frac {{\mathrm e}^{x} x^{4}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (x^{4}-x^{3}+x^{2}+2 c_{1} -x \right ) {\mathrm e}^{4 x}+2 c_{3} {\mathrm e}^{2 x}+2 c_{2} \right ) {\mathrm e}^{-3 x}}{2} \]

Problem 1503

ODE	\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-2 y={\mathrm e}^{x} \left (15 x^{2}+34 x +14\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{\left (-1-i\right ) x} c_{2} +{\mathrm e}^{\left (-1+i\right ) x} c_{3} +x^{2} {\mathrm e}^{x}+{\mathrm e}^{x} x^{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} \cos \left (x \right )+c_{3} \sin \left (x \right )\right ) {\mathrm e}^{-x}+{\mathrm e}^{x} \left (x^{3}+x^{2}+c_{1} \right ) \]

Problem 1504

ODE	\[ \boxed {4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y=-{\mathrm e}^{-2 x} \left (1-15 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-\frac {x}{2}}+{\mathrm e}^{\frac {x}{2}} c_{3} +\frac {x^{2} {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{-2 x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 c_{3} {\mathrm e}^{\frac {5 x}{2}}+2 c_{2} {\mathrm e}^{\frac {3 x}{2}}+x^{2}+2 c_{1} +2 x \right ) {\mathrm e}^{-2 x}}{2} \]

Problem 1505

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

Problem 1506

ODE	\[ \boxed {2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y={\mathrm e}^{2 x} \left (17+30 x \right )} \]
program solution	\[ y = {\mathrm e}^{-\frac {x}{2}} c_{3} +{\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right )+\frac {x^{2} {\mathrm e}^{2 x}}{2}+{\mathrm e}^{2 x} x^{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} c_{2} +{\mathrm e}^{2 x} \left (x^{3}+\frac {1}{2} x^{2}+c_{1} +c_{3} x \right ) \]

Problem 1507

ODE	\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y=2 \,{\mathrm e}^{3 x} \left (11-24 x \right )} \]
program solution	\[ y = {\mathrm e}^{3 x} \left (c_{3} x +c_{2} \right )+c_{1} {\mathrm e}^{-x}+\frac {17 x^{2} {\mathrm e}^{3 x}}{4}-2 x^{3} {\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-8 x^{3}+4 c_{3} x +17 x^{2}+4 c_{2} \right ) {\mathrm e}^{3 x}}{4}+{\mathrm e}^{-x} c_{1} \]

Problem 1508

ODE	\[ \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y=2 \,{\mathrm e}^{4 x} \left (13+15 x \right )} \]
program solution	\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{-x}+2 \,{\mathrm e}^{4 x} x^{2}+{\mathrm e}^{4 x} x^{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (x^{3}+c_{3} x +2 x^{2}+c_{2} \right ) {\mathrm e}^{4 x}+{\mathrm e}^{-x} c_{1} \]

Problem 1509

ODE	\[ \boxed {8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y={\mathrm e}^{\frac {x}{2}} \left (4 x +1\right )} \]
program solution	\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+\frac {x^{3} {\mathrm e}^{\frac {x}{2}}}{48}+\frac {x^{4} {\mathrm e}^{\frac {x}{2}}}{48} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{4}+x^{3}+\left (48 c_{2} +\frac {3}{16}\right ) x^{2}+48 c_{3} x +48 c_{1} \right ) {\mathrm e}^{\frac {x}{2}}}{48} \]

Problem 1510

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y=-3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right )} \]
program solution	\[ y = {\mathrm e}^{-3 x} \left (\left (c_{3} x +c_{2} \right ) {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{x}+c_{4} \right )-6 x \,{\mathrm e}^{-x}+3 x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \left (\left (x -1\right )^{2} {\mathrm e}^{2 x}+\frac {\left (c_{4} x +c_{1} \right ) {\mathrm e}^{4 x}}{3}+\frac {c_{3} {\mathrm e}^{x}}{3}+\frac {c_{2}}{3}\right ) {\mathrm e}^{-3 x} \]

Problem 1511

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y=-3 \,{\mathrm e}^{2 x} \left (11+12 x \right )} \]
program solution	\[ y = {\mathrm e}^{-2 x} \left ({\mathrm e}^{3 x} c_{4} +{\mathrm e}^{x} \left (c_{2} x +c_{1} \right )+c_{3} \right )-x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (-{\mathrm e}^{4 x} x +{\mathrm e}^{4 x}+c_{1} {\mathrm e}^{3 x}+c_{4} x \,{\mathrm e}^{x}+c_{3} {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{-2 x} \]

Problem 1512

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right )} \]
program solution	\[ y = c_{1} +{\mathrm e}^{-4 x} c_{2} +{\mathrm e}^{\left (-2+2 i\right ) x} c_{3} +{\mathrm e}^{\left (-2-2 i\right ) x} c_{4} +x^{2} {\mathrm e}^{-2 x}-x^{3} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x +{\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-c_{2} -c_{3} \right ) \cos \left (2 x \right )+\left (c_{2} -c_{3} \right ) \sin \left (2 x \right )-4 x^{3}+4 x^{2}+4 x +4\right ) {\mathrm e}^{-2 x}}{4}-\frac {{\mathrm e}^{-4 x} c_{1}}{4}+c_{4} \]

Problem 1513

ODE	\[ \boxed {4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y=-{\mathrm e}^{x} \left (1-6 x \right )} \]
program solution	\[ y = \left (\left (c_{4} x +c_{3} \right ) {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{3 x}+c_{1} \right ) {\mathrm e}^{-x}-\frac {x \,{\mathrm e}^{x}}{3}+\frac {{\mathrm e}^{x}}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} \left (\left (c_{4} x +c_{3} \right ) {\mathrm e}^{\frac {x}{2}}-\frac {{\mathrm e}^{2 x} x}{3}+c_{2} {\mathrm e}^{3 x}+c_{1} +\frac {{\mathrm e}^{2 x}}{3}\right ) \]

Problem 1514

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

Problem 1515

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y={\mathrm e}^{2 x} \left (x^{4}+x +24\right )} \]
program solution	\[ y = {\mathrm e}^{-\frac {x \left (-2+\left (-1+i\right ) \sqrt {2}\right )}{2}} c_{1} +{\mathrm e}^{\frac {x \left (2+\left (-1+i\right ) \sqrt {2}\right )}{2}} c_{2} +{\mathrm e}^{\frac {x \left (2+\left (1+i\right ) \sqrt {2}\right )}{2}} c_{3} +{\mathrm e}^{-\frac {x \left (-2+\left (1+i\right ) \sqrt {2}\right )}{2}} c_{4} +\frac {49 x \,{\mathrm e}^{2 x}}{2}+6 x^{2} {\mathrm e}^{2 x}-4 \,{\mathrm e}^{2 x} x^{3}+\frac {{\mathrm e}^{2 x} x^{4}}{2}-31 \,{\mathrm e}^{2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {\left (2+\sqrt {2}\right ) x}{2}} \left (\cos \left (\frac {\sqrt {2}\, x}{2}\right ) c_{1} +\sin \left (\frac {\sqrt {2}\, x}{2}\right ) c_{2} \right )+\left (\cos \left (\frac {\sqrt {2}\, x}{2}\right ) c_{3} +\sin \left (\frac {\sqrt {2}\, x}{2}\right ) c_{4} \right ) {\mathrm e}^{-\frac {\left (\sqrt {2}-2\right ) x}{2}}+\frac {{\mathrm e}^{2 x} \left (x^{4}-8 x^{3}+12 x^{2}+49 x -62\right )}{2} \]

Problem 1516

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

Problem 1517

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{\left (-1-i\right ) x} c_{3} +{\mathrm e}^{\left (-1+i\right ) x} c_{4} +\frac {x \,{\mathrm e}^{2 x}}{6}-\frac {{\mathrm e}^{2 x} x^{3}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{3} +c_{4} \sin \left (x \right )+c_{1} \right ) {\mathrm e}^{-x}-\frac {{\mathrm e}^{2 x} \left (x^{3}-6 c_{2} -x \right )}{6} \]

Problem 1518

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

Problem 1519

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

Problem 1520

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y={\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right )} \]
program solution	\[ y = \left (c_{2} x +c_{1} \right ) {\mathrm e}^{-x}+{\mathrm e}^{2 x} \left (c_{4} x +c_{3} \right )+\frac {x^{2} {\mathrm e}^{2 x}}{6}+\frac {{\mathrm e}^{2 x} x^{3}}{6}+\frac {{\mathrm e}^{2 x} x^{4}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{4}+x^{3}+6 c_{4} x +x^{2}+6 c_{2} \right ) {\mathrm e}^{2 x}}{6}+{\mathrm e}^{-x} \left (c_{3} x +c_{1} \right ) \]

Problem 1521

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }={\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right )} \]
program solution	\[ y = {\mathrm e}^{2 x} \left (c_{4} x +c_{3} \right )+c_{1} {\mathrm e}^{-x}+c_{2} +\frac {x^{2} {\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x} x^{3}}{6}+\frac {{\mathrm e}^{2 x} x^{4}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 x^{4}+2 x^{3}+6 x^{2}+\left (6 c_{3} -6\right ) x +6 c_{2} -3 c_{3} +3\right ) {\mathrm e}^{2 x}}{12}-{\mathrm e}^{-x} c_{1} +c_{4} \]

Problem 1522

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y=\left (x +1\right ) {\mathrm e}^{x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{x} \left (c_{4} x^{2}+c_{3} x +c_{2} \right )+\frac {{\mathrm e}^{x} x^{3}}{24}+\frac {{\mathrm e}^{x} x^{4}}{48} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} c_{2} +\frac {{\mathrm e}^{x} \left (x^{4}+48 c_{4} x^{2}+2 x^{3}+48 c_{3} x +48 c_{1} \right )}{48} \]

Problem 1523

ODE	\[ \boxed {2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y={\mathrm e}^{x} \left (11+12 x \right )} \]
program solution	\[ y = {\mathrm e}^{-\frac {x}{2}} c_{4} +{\mathrm e}^{x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+\frac {{\mathrm e}^{x} x^{3}}{6}+\frac {{\mathrm e}^{x} x^{4}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{4} {\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{x} \left (x^{4}+6 c_{3} x^{2}+x^{3}+6 c_{2} x +6 c_{1} \right )}{6} \]

Problem 1524

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right )} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+c_{4} -\frac {x^{5} {\mathrm e}^{-x}}{6}-\frac {{\mathrm e}^{-x} x^{3}}{6}+\frac {{\mathrm e}^{-x} x^{4}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-x^{5}+x^{4}-x^{3}+\left (-6 c_{3} -3\right ) x^{2}+\left (-6 c_{2} -12 c_{3} -6\right ) x -6 c_{1} -6 c_{2} -12 c_{3} -6\right ) {\mathrm e}^{-x}}{6}+c_{4} \]

Problem 1525

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right )} \]
program solution	\[ y = \left (c_{4} x^{2}+c_{3} x +c_{2} \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{x}-\frac {x^{5} {\mathrm e}^{2 x}}{12}+\frac {{\mathrm e}^{2 x} x^{3}}{6}+\frac {{\mathrm e}^{2 x} x^{4}}{12} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (\left (x^{5}-x^{4}-12 c_{4} x^{2}-2 x^{3}-12 c_{3} x -12 c_{2} \right ) {\mathrm e}^{x}-12 c_{1} \right )}{12} \]

Problem 1526

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{2 x}+\cos \left (x \right ) {\mathrm e}^{-x}+2 \sin \left (x \right ) {\mathrm e}^{-x}+x \cos \left (x \right ) {\mathrm e}^{-x}-\sin \left (x \right ) x \,{\mathrm e}^{-x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{3 x}+c_{3} {\mathrm e}^{4 x}+\left (\left (x +1\right ) \cos \left (x \right )-\sin \left (x \right ) \left (-2+x \right )\right ) {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{-2 x} \]

Problem 1527

ODE	\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right )} \]
program solution	\[ y = \left ({\mathrm e}^{4 x} c_{3} +c_{1} {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{-2 x}+{\mathrm e}^{-x} \cos \left (2 x \right )+{\mathrm e}^{-x} \sin \left (2 x \right )-{\mathrm e}^{-x} \cos \left (2 x \right ) x +{\mathrm e}^{-x} \sin \left (2 x \right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\left ({\mathrm e}^{x} \left (x -1\right ) \cos \left (2 x \right )-\left (x +1\right ) {\mathrm e}^{x} \sin \left (2 x \right )-c_{3} {\mathrm e}^{4 x}+\left (-c_{2} +\frac {5}{3}\right ) {\mathrm e}^{x}-c_{1} \right ) {\mathrm e}^{-2 x} \]

Problem 1528

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{-i \sqrt {2}\, x} c_{2} +{\mathrm e}^{i \sqrt {2}\, x} c_{3} +{\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{2 x} \cos \left (x \right ) x -{\mathrm e}^{2 x} \cos \left (x \right ) x^{2}+2 \,{\mathrm e}^{2 x} \sin \left (x \right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {2}\, \left (\int {\mathrm e}^{2 x} \left (\sqrt {2}\, \cos \left (\sqrt {2}\, x \right )-\sin \left (\sqrt {2}\, x \right )\right ) \left (\left (-9 x^{2}-13 x -2\right ) \sin \left (x \right )+\left (x^{2}-5 x -27\right ) \cos \left (x \right )\right )d x \right ) \cos \left (\sqrt {2}\, x \right )}{6}-\frac {\sqrt {2}\, \left (\int -{\mathrm e}^{2 x} \left (\sqrt {2}\, \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right )\right ) \left (\left (-9 x^{2}-13 x -2\right ) \sin \left (x \right )+\left (x^{2}-5 x -27\right ) \cos \left (x \right )\right )d x \right ) \sin \left (\sqrt {2}\, x \right )}{6}+c_{2} \cos \left (\sqrt {2}\, x \right )+c_{3} \sin \left (\sqrt {2}\, x \right )+\frac {\left (5 \left (-x^{2}+x +3\right ) \cos \left (x \right )+4 \left (x^{2}+\frac {5}{2} x +\frac {7}{4}\right ) \sin \left (x \right )\right ) {\mathrm e}^{2 x}}{3}+{\mathrm e}^{x} c_{1} \]

Problem 1529

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{-i x} c_{2} +{\mathrm e}^{i x} c_{3} +\frac {61 \,{\mathrm e}^{x} \cos \left (2 x \right )}{50}-\frac {27 \,{\mathrm e}^{x} \sin \left (2 x \right )}{50}+\frac {11 \cos \left (2 x \right ) {\mathrm e}^{x} x}{10}+\frac {{\mathrm e}^{x} \sin \left (2 x \right ) x^{2}}{2}+\frac {3 \sin \left (2 x \right ) {\mathrm e}^{x} x}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (x^{2}+\frac {3}{5} x -\frac {27}{25}\right ) \sin \left (2 x \right )}{2}+\frac {\left (55 x +61\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{50}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} +c_{3} {\mathrm e}^{2 x} \]

Problem 1530

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y=8 \cos \left (2 x \right )-16 \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{-2 i x} c_{2} +{\mathrm e}^{2 i x} c_{3} +\frac {\left (208 x +99\right ) \cos \left (2 x \right )}{338}+\frac {14 \left (-6+13 x \right ) \sin \left (2 x \right )}{169} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (169 c_{1} +104 x +56\right ) \cos \left (2 x \right )}{169}+\frac {\left (182 x +169 c_{3} -136\right ) \sin \left (2 x \right )}{169}+{\mathrm e}^{-3 x} c_{2} \]

Problem 1531

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+2 y={\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12 x +12\right ) \sin \left (x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{\left (1+i\right ) x} c_{2} +{\mathrm e}^{\left (1-i\right ) x} c_{3} +\frac {23 \,{\mathrm e}^{x} \left (\left (\frac {20}{23} x^{2}+\frac {25}{23}+i+\frac {20}{23} x \right ) \cos \left (x \right )-\frac {21 \left (-\frac {20}{21} x^{2}+\frac {65}{21}+i-\frac {20}{7} x \right ) \sin \left (x \right )}{23}\right )}{20} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +{\mathrm e}^{x} \left (\left (x^{2}+x +c_{2} +\frac {22}{5}\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x^{2}+3 x +\frac {1}{5}+c_{3} \right )\right ) \]

Problem 1532

ODE	\[ \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{\left (2+2 i\right ) x} c_{2} +{\mathrm e}^{\left (2-2 i\right ) x} c_{3} -\frac {{\mathrm e}^{2 x} \left (\left (x^{2}-3 x -\frac {21}{20}\right ) \cos \left (2 x \right )-\left (x -\frac {37}{20}\right ) \sin \left (2 x \right )\right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-20 x^{2}+40 c_{2} +60 x -83\right ) \cos \left (2 x \right )+20 \sin \left (2 x \right ) \left (x +2 c_{3} -\frac {47}{10}\right )\right ) {\mathrm e}^{2 x}}{40}+c_{1} {\mathrm e}^{3 x} \]

Problem 1533

ODE	\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }=-{\mathrm e}^{3 x} \left (\left (-3 x +2\right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right )} \]
program solution	\[ y = c_{1} +{\mathrm e}^{\left (3-3 i\right ) x} c_{2} +{\mathrm e}^{\left (3+3 i\right ) x} c_{3} -\frac {{\mathrm e}^{3 x} \left (18 \cos \left (3 x \right ) x^{2}+18 x \sin \left (3 x \right )-4 \sin \left (3 x \right )+7 \cos \left (3 x \right )\right )}{216} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-3 x^{2}+6 c_{1} -6 c_{2} -1\right ) \cos \left (3 x \right )-3 \sin \left (3 x \right ) \left (x -2 c_{1} -2 c_{2} +\frac {1}{9}\right )\right ) {\mathrm e}^{3 x}}{36}+c_{3} \]

Problem 1534

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

Problem 1535

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

Problem 1536

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y={\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{\left (2-i\right ) x} c_{3} +{\mathrm e}^{\left (2+i\right ) x} c_{4} +{\mathrm e}^{2 x} \cos \left (2 x \right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x} x \cos \left (x \right )^{2}+c_{4} \sin \left (x \right ) {\mathrm e}^{x}+c_{3} \cos \left (x \right ) {\mathrm e}^{x}-x \,{\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{1} \right ) \]

Problem 1537

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y={\mathrm e}^{-x} \left (\left (-x +4\right ) \cos \left (x \right )-\left (x +5\right ) \sin \left (x \right )\right )} \]
program solution	\[ y = \left (c_{4} x +c_{3} \right ) {\mathrm e}^{-2 x}+\left (c_{2} x +c_{1} \right ) {\mathrm e}^{-x}-\frac {\cos \left (x \right ) {\mathrm e}^{-x}}{2}-\sin \left (x \right ) {\mathrm e}^{-x}-\frac {x \cos \left (x \right ) {\mathrm e}^{-x}}{2}+\frac {\sin \left (x \right ) x \,{\mathrm e}^{-x}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-x -1\right ) \cos \left (x \right )+\sin \left (x \right ) \left (-2+x \right )+2 c_{3} x +2 c_{2} \right ) {\mathrm e}^{-x}}{2}+{\mathrm e}^{-2 x} \left (c_{4} x +c_{1} \right ) \]

Problem 1538

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y=-{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{x}+{\mathrm e}^{\left (-1-i\right ) x} c_{3} +{\mathrm e}^{\left (-1+i\right ) x} c_{4} +\frac {{\mathrm e}^{-x} \left (\left (\frac {41}{10}+i+2 x \right ) \cos \left (x \right )-\frac {\sin \left (x \right ) \left (\frac {38}{5}+i-8 x \right )}{2}\right )}{20} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (10 c_{1} {\mathrm e}^{3 x}+\left (\left (x +10 c_{3} +\frac {14}{5}\right ) \cos \left (x \right )+2 \sin \left (x \right ) \left (x +5 c_{4} -\frac {1}{5}\right )\right ) {\mathrm e}^{x}+10 c_{2} \right ) {\mathrm e}^{-2 x}}{10} \]

Problem 1539

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y={\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{\left (1+2 i\right ) x} c_{3} +{\mathrm e}^{\left (1-2 i\right ) x} c_{4} +\frac {{\mathrm e}^{x} \left (60 x \cos \left (2 x \right )-20 x \sin \left (2 x \right )-11 \cos \left (2 x \right )-73 \sin \left (2 x \right )\right )}{800} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {3 \,{\mathrm e}^{x} \left (x +\frac {40 c_{3}}{3}+\frac {1}{15}\right ) \cos \left (2 x \right )}{40}-\frac {{\mathrm e}^{x} \left (x -40 c_{4} +\frac {39}{10}\right ) \sin \left (2 x \right )}{40}+c_{2} {\mathrm e}^{2 x}+\frac {{\mathrm e}^{x} \left (8 c_{1} +1\right )}{8} \]

Problem 1540

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-3 x}+{\mathrm e}^{\left (-2+3 i\right ) x} c_{3} +{\mathrm e}^{\left (-2-3 i\right ) x} c_{4} -\frac {{\mathrm e}^{-2 x} \left (\left (x^{2}-x -\frac {11}{30}\right ) \cos \left (3 x \right )-\left (x^{2}+x -\frac {11}{30}\right ) \sin \left (3 x \right )\right )}{8} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-30 x^{2}+240 c_{3} +30 x +11\right ) \cos \left (3 x \right )+30 \left (x^{2}+x +8 c_{4} -\frac {11}{30}\right ) \sin \left (3 x \right )\right ) {\mathrm e}^{-2 x}}{240}+c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{-x} c_{2} \]

Problem 1541

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y={\mathrm e}^{x} \left (\left (8 x +7\right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{\left (1+2 i\right ) x} c_{3} +{\mathrm e}^{\left (1-2 i\right ) x} c_{4} -\frac {{\mathrm e}^{x} \left (\left (x^{2}+x +\frac {21}{20}\right ) \sin \left (2 x \right )+\frac {17 \cos \left (2 x \right )}{20}\right )}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (x^{2}+x -4 c_{4} +\frac {23}{4}\right ) \sin \left (2 x \right )}{4}+\frac {\left (4 c_{3} +3\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{4}+c_{2} {\mathrm e}^{2 x}+\frac {{\mathrm e}^{x} \left (2 c_{1} +7\right )}{2} \]

Problem 1542

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

Problem 1543

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y={\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right )} \]
program solution	\[ y = \left (c_{4} x +c_{3} \right ) {\mathrm e}^{\left (2-2 i\right ) x}+{\mathrm e}^{\left (2+2 i\right ) x} \left (c_{2} x +c_{1} \right )-\frac {{\mathrm e}^{2 x} \left (-\left (\int \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \left (2 x \cos \left (2 x \right )-\sin \left (2 x \right )\right )d x \right ) \cos \left (2 x \right )-\left (\int \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \left (\cos \left (2 x \right )+2 x \sin \left (2 x \right )\right )d x \right ) \sin \left (2 x \right )+x \left (\cos \left (2 x \right ) \left (x +\frac {1}{4}\right )-\left (x -\frac {1}{4}\right ) \sin \left (2 x \right )\right )\right )}{16} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{2 x} \left (\left (x^{2}+\left (-32 c_{3} -\frac {3}{2}\right ) x -32 c_{1} -\frac {41}{4}\right ) \cos \left (2 x \right )-\sin \left (2 x \right ) \left (x^{2}+\left (32 c_{4} +\frac {1}{2}\right ) x +32 c_{2} -\frac {517}{18}\right )\right )}{32} \]

Problem 1544

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (3 x +1\right ) \sin \left (x \right )\right )} \]
program solution	\[ y = \left (c_{2} x +c_{1} \right ) {\mathrm e}^{\left (2-i\right ) x}+{\mathrm e}^{\left (2+i\right ) x} \left (c_{4} x +c_{3} \right )+\frac {9 \left (-\frac {8 \left (\int \left (-\sin \left (x \right )^{2}+3 \cos \left (x \right ) \left (x^{2}+\frac {1}{3} x +1\right ) \sin \left (x \right )-3 x \right )d x \right ) \left (i \sin \left (x \right )+\cos \left (x \right )\right )}{9}+\frac {8 \left (\cos \left (x \right )-i \sin \left (x \right )\right ) \left (\int \left (-3 \sin \left (x \right ) x -\sin \left (x \right )+3 \cos \left (x \right )\right ) \left (x \cos \left (x \right )-\sin \left (x \right )\right )d x \right )}{9}+\frac {16 \left (\int -3 \left (\sin \left (x \right ) x +\cos \left (x \right )\right ) \left (\left (x +\frac {1}{3}\right ) \sin \left (x \right )-\cos \left (x \right )\right )d x \right ) \sin \left (x \right )}{9}-x \left (\frac {\left (5-\frac {2}{3} i-4 x^{2}-\frac {8}{3} x \right ) \sin \left (x \right )}{3}+\cos \left (x \right ) \left (\frac {2}{9}-i+4 x \right )\right )\right ) {\mathrm e}^{2 x}}{32} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (\left (x^{3}+x^{2}+\left (8 c_{4} +3\right ) x +8 c_{2} -2\right ) \sin \left (x \right )+8 \cos \left (x \right ) \left (\left (c_{3} +\frac {1}{4}\right ) x +c_{1} +\frac {9}{16}\right )\right )}{8} \]

Problem 1545

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

Problem 1546

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

Problem 1547

ODE	\[ \boxed {y^{\prime \prime \prime }-y^{\prime }=-2-2 x +4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} +{\mathrm e}^{x} c_{3} +2 x \,{\mathrm e}^{x}-3 x \,{\mathrm e}^{-x}+4 \,{\mathrm e}^{3 x}+2 x +x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-6 x -2 c_{2} -9\right ) {\mathrm e}^{-x}}{2}+4 \,{\mathrm e}^{3 x}+\left (2 x -3+c_{1} \right ) {\mathrm e}^{x}+x^{2}+2 x +c_{3} \]

Problem 1548

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{\left (1+2 i\right ) x} c_{2} +{\mathrm e}^{\left (1-2 i\right ) x} c_{3} +1+\frac {\left (10 x -11\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{10}+\frac {2 \left (-2+5 x \right ) {\mathrm e}^{2 x}}{5}+\frac {\left (-40 x -21\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{20} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 1+{\mathrm e}^{x} \left (x -\frac {8}{5}+c_{2} \right ) \cos \left (2 x \right )+\frac {\left (-4+10 x +5 c_{1} \right ) {\mathrm e}^{2 x}}{5}-2 \left (x -\frac {c_{3}}{2}+\frac {13}{20}\right ) {\mathrm e}^{x} \sin \left (2 x \right ) \]

Problem 1549

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y=12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right )} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+2 \,{\mathrm e}^{-x} x^{3}-\cos \left (2 x \right )+\sin \left (2 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{3} x^{2}+2 x^{3}+c_{2} x +c_{1} \right ) {\mathrm e}^{-x}-\cos \left (2 x \right )+\sin \left (2 x \right ) \]

Problem 1550

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

Problem 1551

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

Problem 1552

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right )} \]
program solution	\[ y = {\mathrm e}^{\left (1+2 i\right ) x} c_{1} +{\mathrm e}^{\left (1-2 i\right ) x} c_{2} +{\mathrm e}^{\left (1+i\right ) x} c_{3} +{\mathrm e}^{\left (1-i\right ) x} c_{4} -\frac {{\mathrm e}^{x} \left (\left (\int \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \sin \left (2 x \right )d x \right ) \cos \left (2 x \right )+2 \left (\int \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \cos \left (x \right )d x \right ) \sin \left (x \right )-\left (\int \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \cos \left (2 x \right )d x \right ) \sin \left (2 x \right )-2 \left (\int \left (\sin \left (x \right )+4 \cos \left (x \right )^{2}-2\right ) \sin \left (x \right )d x \right ) \cos \left (x \right )\right )}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (\left (6 c_{3} +\frac {7}{3}\right ) \cos \left (2 x \right )+\left (x +6 c_{4} \right ) \sin \left (2 x \right )+\left (x +6 c_{1} \right ) \cos \left (x \right )+6 \left (\frac {1}{9}+c_{2} \right ) \sin \left (x \right )\right )}{6} \]

Problem 1553

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y=2 \left (x +1\right ) {\mathrm e}^{x}+{\mathrm e}^{-2 x}} \]
program solution	\[ y = {\mathrm e}^{-2 x} \left (\left (c_{4} x +c_{3} \right ) {\mathrm e}^{3 x}+c_{2} x +c_{1} \right )+\frac {x^{2} {\mathrm e}^{-2 x}}{18}+\frac {x^{2} {\mathrm e}^{x}}{27}+\frac {{\mathrm e}^{x} x^{3}}{27} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x} \left (\left (x^{3}+x^{2}+\left (27 c_{3} -2\right ) x +27 c_{1} +\frac {10}{9}\right ) {\mathrm e}^{3 x}+\frac {3 x^{2}}{2}+\left (27 c_{4} +2\right ) x +27 c_{2} +1\right )}{27} \]

Problem 1554

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

Problem 1555

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x}} \]
program solution	\[ y = {\mathrm e}^{-x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right )+{\mathrm e}^{-2 x} c_{4} +{\mathrm e}^{-2 x} x +{\mathrm e}^{-x} x^{3}+{\mathrm e}^{-x} x^{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (x^{4}+x^{3}+\left (c_{4} -3\right ) x^{2}+\left (c_{3} +6\right ) x +c_{2} -6\right ) {\mathrm e}^{-x}+{\mathrm e}^{-2 x} \left (x +c_{1} +3\right ) \]

Problem 1556

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right )} \]
program solution	\[ y = {\mathrm e}^{\left (1-i\right ) x} c_{4} +{\mathrm e}^{\left (1+i\right ) x} c_{3} +{\mathrm e}^{x} \left (c_{2} x +c_{1} \right )+{\mathrm e}^{x} \left (x \cos \left (x \right )-12 x +\sin \left (x \right ) x -15 \sin \left (x \right )+2 x^{3}+2 \cos \left (x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{x} \left (\left (x +c_{3} +3\right ) \cos \left (x \right )+\left (c_{4} +x -2\right ) \sin \left (x \right )+2 x^{3}+\left (c_{2} -12\right ) x +c_{1} \right ) \]

Problem 1557

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

Problem 1558

ODE	\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-2 y=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{\left (-1-i\right ) x} c_{2} +{\mathrm e}^{\left (-1+i\right ) x} c_{3} -x \,{\mathrm e}^{3 x}-\frac {x^{2} {\mathrm e}^{3 x}}{2}+{\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x} \left (\left (x^{2}+2 x -2\right ) {\mathrm e}^{4 x}-2 c_{1} {\mathrm e}^{2 x}-2 c_{2} \cos \left (x \right )-2 c_{3} \sin \left (x \right )\right )}{2} \]

Problem 1559

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

Problem 1560

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

Problem 1561

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

Problem 1562

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

Problem 1563

ODE	\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{x} c_{3} +{\mathrm e}^{-2 x} \cos \left (x \right )+\frac {3 \,{\mathrm e}^{-2 x} \sin \left (x \right )}{2}+\frac {{\mathrm e}^{-2 x} \cos \left (x \right ) x}{2}-2 \,{\mathrm e}^{-2 x} \sin \left (x \right ) x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 c_{1} {\mathrm e}^{3 x}+\left (2+x \right ) \cos \left (x \right )+\left (-4 x +3\right ) \sin \left (x \right )+2 c_{3} {\mathrm e}^{x}+2 c_{2} \right ) {\mathrm e}^{-2 x}}{2} \]

Problem 1564

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right )} \]
program solution	\[ y = c_{2} {\mathrm e}^{x}+c_{1} +{\mathrm e}^{\left (1+i\right ) x} c_{3} +{\mathrm e}^{\left (1-i\right ) x} c_{4} -\sin \left (2 x \right ) {\mathrm e}^{x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\left (-4 x \sin \left (x \right )+c_{2} -c_{3} \right ) \cos \left (x \right )+\left (c_{2} +c_{3} \right ) \sin \left (x \right )+2 c_{1} +3\right ) {\mathrm e}^{x}}{2}+c_{4} \]

Problem 1565

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y={\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right )} \]
program solution	\[ y = \left (c_{4} x +c_{3} \right ) {\mathrm e}^{\left (1-2 i\right ) x}+{\mathrm e}^{\left (1+2 i\right ) x} \left (c_{2} x +c_{1} \right )-\frac {{\mathrm e}^{x} \left (24 x^{3} \cos \left (2 x \right )+16 \cos \left (2 x \right ) x^{2}+4 i \left (\int \left (\left (-12 x^{2}-4 x \right ) \cos \left (2 x \right )^{2}+2 \sin \left (2 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )^{2}\right )d x \right ) \sin \left (2 x \right )+2 i \left (\int \left (\left (12 x^{2}+4 x +3\right ) \cos \left (4 x \right )+12 x^{2}+4 x -2 \sin \left (4 x \right )-3\right )d x \right ) \sin \left (2 x \right )+36 \sin \left (2 x \right ) x^{2}+4 \left (\int \left (\left (-12 x^{2}-4 x \right ) \cos \left (2 x \right )^{2}+2 \sin \left (2 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )^{2}\right )d x \right ) \cos \left (2 x \right )-2 \left (\int \left (\left (12 x^{2}+4 x +3\right ) \cos \left (4 x \right )+12 x^{2}+4 x -2 \sin \left (4 x \right )-3\right )d x \right ) \cos \left (2 x \right )-3 x \cos \left (2 x \right )-4 \left (\int \left (\left (12 x^{2}+4 x +3\right ) \sin \left (4 x \right )+12 x +2 \cos \left (4 x \right )+2\right )d x \right ) \sin \left (2 x \right )+4 x \sin \left (2 x \right )\right )}{128} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (\left (x^{3}+x^{2}+\left (-16 c_{3} +\frac {63}{2}\right ) x -16 c_{1} -\frac {41}{4}\right ) \cos \left (2 x \right )-16 \left (\left (c_{4} +\frac {1}{32}\right ) x +c_{2} +\frac {1111}{192}\right ) \sin \left (2 x \right )\right )}{16} \]

Problem 1566

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y=2 \,{\mathrm e}^{x} \left (1-6 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 7, y^{\prime \prime }\left (0\right ) = 9] \end {align*}
program solution	\[ y = x^{2} {\mathrm e}^{x}+2 \,{\mathrm e}^{x}-{\mathrm e}^{-2 x}+{\mathrm e}^{3 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left ({\mathrm e}^{5 x}+x^{2} {\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-2 x} \]

Problem 1567

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

Problem 1568

ODE	\[ \boxed {4 y^{\prime \prime \prime }-3 y^{\prime }-y={\mathrm e}^{-\frac {x}{2}} \left (-3 x +2\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 15, y^{\prime \prime }\left (0\right ) = -17] \end {align*}
program solution	\[ y = \frac {\left (x^{3}+192 x \right ) {\mathrm e}^{-\frac {x}{2}}}{12}-{\mathrm e}^{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (x^{3}+192 x \right ) {\mathrm e}^{-\frac {x}{2}}}{12}-{\mathrm e}^{x} \]

Problem 1569

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y={\mathrm e}^{-x} \left (20-12 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4, y^{\prime \prime }\left (0\right ) = 7, y^{\prime \prime \prime }\left (0\right ) = -22] \end {align*}
program solution	\[ y = \left (-x^{3}+2 x^{2}-x +2\right ) {\mathrm e}^{-x}+\cos \left (x \right )-\sin \left (x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (-x^{3}+2 x^{2}-x +2\right ) {\mathrm e}^{-x}+\cos \left (x \right )-\sin \left (x \right ) \]

Problem 1570

ODE	\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y=30 \cos \left (x \right )-10 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4, y^{\prime \prime }\left (0\right ) = 16] \end {align*}
program solution	\[ y = {\mathrm e}^{-2 x}+\left (2-x \right ) \cos \left (x \right )+\left (7 x -1\right ) \sin \left (x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-2 x}+\left (2-x \right ) \cos \left (x \right )+\left (7 x -1\right ) \sin \left (x \right ) \]

Problem 1571

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

Problem 1572

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

Problem 1573

ODE	\[ \boxed {4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y=30 x^{2}} \]
program solution	\[ y = \frac {c_{1} x^{\frac {5}{2}}+c_{3} x +c_{2}}{\sqrt {x}}+2 x^{2} \left (-\frac {16}{15}+\ln \left (x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (c_{1} +2 \ln \left (x \right )-\frac {32}{15}\right ) x^{\frac {5}{2}}+c_{3} x +c_{2}}{\sqrt {x}} \]

Problem 1574

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

Problem 1575

ODE	\[ \boxed {16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y=96 x^{\frac {5}{2}}} \]
program solution	\[ y = \frac {c_{3} x^{3}+c_{4} x^{2}+c_{2} x +c_{1}}{x^{\frac {3}{2}}}+\frac {x^{\frac {5}{2}}}{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {4 c_{4} x^{3}+x^{4}+4 c_{3} x^{2}+4 c_{2} x +4 c_{1}}{4 x^{\frac {3}{2}}} \]

Problem 1576

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y=x^{4}} \]
program solution	\[ y = x \left (c_{4} x^{3}+c_{3} x^{2}+c_{2} x +c_{1} \right )+\frac {x^{4} \left (-11+6 \ln \left (x \right )\right )}{36} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\frac {x^{3} \ln \left (x \right )}{6}+\left (c_{4} -\frac {11}{36}\right ) x^{3}+c_{3} x^{2}+c_{2} x +c_{1} \right ) x \]

Problem 1577

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y=12 x^{2}} \]
program solution	\[ y = \frac {c_{1}}{x}+\frac {c_{2}}{x^{2}}+c_{3} x +c_{4} x^{2}+x^{2} \left (-\frac {19}{12}+\ln \left (x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {12 x^{4} \ln \left (x \right )+\left (12 c_{2} -15\right ) x^{4}+12 c_{3} x^{3}+2 c_{1} x +12 c_{4}}{12 x^{2}} \]

Problem 1578

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

Problem 1579

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y=x^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1, y^{\prime \prime }\left (1\right ) = 7] \end {align*}
program solution	\[ y = \frac {\left (x \ln \left (x \right )^{2}+4 x \ln \left (x \right )-2 x +2\right ) x^{2}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2} \left (\ln \left (x \right )^{2} x +4 x \ln \left (x \right )-2 x +2\right )}{2} \]

Problem 1580

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y=9 x^{4}} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 1, y^{\prime \prime }\left (1\right ) = 5] \end {align*}
program solution	\[ y = \frac {3 \ln \left (x \right )^{2} x^{4}}{2}+2 \ln \left (x \right ) x^{4}-x^{4}+3 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x^{4}+\frac {3 \ln \left (x \right )^{2} x^{4}}{2}+2 x^{4} \ln \left (x \right )+3 x \]

Problem 1581

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=x \left (x +1\right )} \] With initial conditions \begin {align*} \left [y \left (-1\right ) = -6, y^{\prime }\left (-1\right ) = {\frac {43}{6}}, y^{\prime \prime }\left (-1\right ) = -{\frac {5}{2}}\right ] \end {align*}
program solution	\[ y = -\frac {\left (2 i x \pi -3 i \pi -2 x \ln \left (x \right )+3 \ln \left (x \right )+12 x -24\right ) x}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x \left (-2 i \pi x +2 x \ln \left (x \right )+3 i \pi -3 \ln \left (x \right )-12 x +24\right )}{6} \]

Problem 1582

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y=9 x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = -7, y^{\prime }\left (1\right ) = -11, y^{\prime \prime }\left (1\right ) = -5, y^{\prime \prime \prime }\left (1\right ) = 6] \end {align*}
program solution	\[ y = x^{2} \left (-7+3 \ln \left (x \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{2} \left (-7+3 \ln \left (x \right )\right ) \]

Problem 1583

ODE	\[ \boxed {4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y=6 x} \] With initial conditions \begin {align*} \left [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 0, y^{\prime \prime }\left (1\right ) = 4, y^{\prime \prime \prime }\left (1\right ) = -{\frac {37}{4}}\right ] \end {align*}
program solution	\[ y = \frac {x^{\frac {5}{2}} \ln \left (x \right )+x^{\frac {5}{2}}-x^{2}+\sqrt {x}+x}{x^{\frac {3}{2}}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\ln \left (x \right ) x^{\frac {5}{2}}-x^{2}+x^{\frac {5}{2}}+\sqrt {x}+x}{x^{\frac {3}{2}}} \]

Problem 1584

ODE	\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y=40 x^{3}} \] With initial conditions \begin {align*} [y \left (-1\right ) = -1, y^{\prime }\left (-1\right ) = -7, y^{\prime \prime }\left (-1\right ) = -1, y^{\prime \prime \prime }\left (-1\right ) = -31] \end {align*}
program solution	\[ y = \frac {x^{5} \ln \left (x \right )-1+\left (-i \pi -2\right ) x^{5}+x^{3}+x}{x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{5} \ln \left (x \right )-1+\left (-i \pi -2\right ) x^{5}+x^{3}+x}{x^{2}} \]

Problem 1585

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

Problem 1586

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

Problem 1587

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

Problem 1588

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

Problem 1589

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=y_{1} \left (t \right )+2 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )+y_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-t} \\ y_{2} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{-t} \\ \end{align*}

Problem 1590

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=-\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4}\\ y_{2}^{\prime }\left (t \right )&=\frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4} \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-\frac {t}{2}} \\ y_{2} \left (t \right ) &= -c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-\frac {t}{2}} \\ \end{align*}

Problem 1591

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=-\frac {4 y_{1} \left (t \right )}{5}+\frac {3 y_{2} \left (t \right )}{5}\\ y_{2}^{\prime }\left (t \right )&=-\frac {2 y_{1} \left (t \right )}{5}-\frac {11 y_{2} \left (t \right )}{5} \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{-2 t} \\ y_{2} \left (t \right ) &= -\frac {{\mathrm e}^{-t} c_{1}}{3}-2 c_{2} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 1592

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-4 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t} \\ y_{2} \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{t}}{2}+\frac {c_{2} {\mathrm e}^{-3 t}}{2} \\ \end{align*}

Problem 1593

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )-4 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-2 t} \\ y_{2} \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{3 t}}{4}+c_{2} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 1594

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=4 y_{1} \left (t \right )-3 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=2 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t} \\ y_{2} \left (t \right ) &= c_{1} {\mathrm e}^{t}+\frac {2 c_{2} {\mathrm e}^{2 t}}{3} \\ \end{align*}

Problem 1595

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )-3 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{-5 t} \\ y_{2} \left (t \right ) &= -c_{1} {\mathrm e}^{-3 t}-\frac {c_{2} {\mathrm e}^{-5 t}}{3} \\ \end{align*}

Problem 1596

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=y_{1} \left (t \right )-2 y_{2} \left (t \right )-3 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-4 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{-3 t} \\ y_{2} \left (t \right ) &= 4 \,{\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t}+2 c_{3} {\mathrm e}^{-3 t} \\ y_{3} \left (t \right ) &= -{\mathrm e}^{-t} c_{1} -c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{-3 t} \\ \end{align*}

Problem 1597

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-4 y_{1} \left (t \right )-4 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= 2 c_{2} {\mathrm e}^{-16 t}+2 c_{3} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{2 t} \\ y_{2} \left (t \right ) &= c_{2} {\mathrm e}^{-16 t}+c_{3} {\mathrm e}^{2 t} \\ y_{3} \left (t \right ) &= 2 c_{2} {\mathrm e}^{-16 t}-\frac {5 c_{3} {\mathrm e}^{2 t}}{2}-c_{1} {\mathrm e}^{2 t} \\ \end{align*}

Problem 1598

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+8 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-2 t}+c_{3} {\mathrm e}^{2 t} \\ y_{2} \left (t \right ) &= 2 c_{1} {\mathrm e}^{t}-c_{2} {\mathrm e}^{-2 t}+\frac {5 c_{3} {\mathrm e}^{2 t}}{7} \\ y_{3} \left (t \right ) &= -\frac {3 c_{1} {\mathrm e}^{t}}{2}-\frac {4 c_{3} {\mathrm e}^{2 t}}{7} \\ \end{align*}

Problem 1599

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{-5 t} \\ y_{2} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+2 c_{2} {\mathrm e}^{-3 t}+3 c_{3} {\mathrm e}^{-5 t} \\ y_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{-2 t}-c_{2} {\mathrm e}^{-3 t}-\frac {3 c_{3} {\mathrm e}^{-5 t}}{2} \\ \end{align*}

Problem 1600

ODE	\begin {align*} y_{1}^{\prime }\left (t \right )&=4 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=4 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-2 t} \\ y_{2} \left (t \right ) &= \frac {7 c_{1} {\mathrm e}^{3 t}}{11}+c_{2} {\mathrm e}^{-t}+2 c_{3} {\mathrm e}^{-2 t} \\ y_{3} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{3 t}}{11}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-2 t} \\ \end{align*}