2.17.22 Problems 2101 to 2200

Problem 2101

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

Problem 2102

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

Problem 2103

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-4 x}+c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{5 x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{9 x}+c_{1} {\mathrm e}^{7 x}+c_{3} \right ) {\mathrm e}^{-4 x} \]

Problem 2104

ODE	\[ \boxed {y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{5 x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{3 x}+c_{2} {\mathrm e}^{5 x}+c_{3} {\mathrm e}^{x} \]

Problem 2105

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

Problem 2106

ODE	\[ \boxed {2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{3} +{\mathrm e}^{-\frac {x}{2}} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{6 x}+c_{2} {\mathrm e}^{5 x}+c_{4} {\mathrm e}^{\frac {5 x}{2}}+c_{3} \right ) {\mathrm e}^{-3 x} \]

Problem 2107

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

Problem 2108

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

Problem 2109

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

Problem 2110

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

Problem 2111

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{x}+{\mathrm e}^{-3 x} c_{3} +{\mathrm e}^{2 x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{5 x}+c_{4} {\mathrm e}^{4 x}+c_{2} {\mathrm e}^{x}+c_{3} \right ) {\mathrm e}^{-3 x} \]

Problem 2112

ODE	\[ \boxed {y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{x} c_{3} +{\mathrm e}^{2 x} c_{4} +{\mathrm e}^{3 x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{5 x}+c_{2} {\mathrm e}^{4 x}+c_{5} {\mathrm e}^{3 x}+c_{4} {\mathrm e}^{x}+c_{3} \right ) {\mathrm e}^{-2 x} \]

Problem 2113

ODE	\[ \boxed {y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-3 x} c_{3} +{\mathrm e}^{2 x} c_{4} +{\mathrm e}^{3 x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{6 x}+c_{2} {\mathrm e}^{5 x}+c_{5} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x}+c_{4} \right ) {\mathrm e}^{-3 x} \]

Problem 2114

ODE	\[ \boxed {y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }=0} \]
program solution	\[ y = c_{1} +c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{x} c_{3} +{\mathrm e}^{3 x} c_{4} +{\mathrm e}^{-5 x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{8 x}+c_{5} {\mathrm e}^{6 x}+c_{1} {\mathrm e}^{5 x}+c_{4} {\mathrm e}^{3 x}+c_{3} \right ) {\mathrm e}^{-5 x} \]

Problem 2115

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

Problem 2116

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

Problem 2117

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

Problem 2118

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

Problem 2119

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

Problem 2120

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

Problem 2121

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

Problem 2122

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

Problem 2123

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

Problem 2124

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

Problem 2125

ODE	\[ \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} x \,{\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x} \]

Problem 2126

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

Problem 2127

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

Problem 2128

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	\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_{3} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]

Problem 2129

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

Problem 2130

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{i \sqrt {5}\, x} c_{3} +{\mathrm e}^{-i \sqrt {5}\, x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{2} +c_{3} \sin \left (\sqrt {5}\, x \right )+c_{4} \cos \left (\sqrt {5}\, x \right ) \]

Problem 2131

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

Problem 2132

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} x \,{\mathrm e}^{2 x}+{\mathrm e}^{-i \sqrt {2}\, x} c_{3} +{\mathrm e}^{i \sqrt {2}\, x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{4} \cos \left (\sqrt {2}\, x \right )+c_{3} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right ) \]

Problem 2133

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y=0} \]
program solution	\[ y = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =2\right ) x} c_{1} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =3\right ) x} c_{2} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =1\right ) x} c_{3} +{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =4\right ) x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}} \]

Problem 2134

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

Problem 2135

ODE	\[ \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y=0} \]
program solution	\[ y = {\mathrm e}^{\frac {3 x}{2}} c_{1} +{\mathrm e}^{i \sqrt {5}\, x} c_{2} +{\mathrm e}^{-i \sqrt {5}\, x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_{2} \sin \left (\sqrt {5}\, x \right )+c_{3} \cos \left (\sqrt {5}\, x \right ) \]

Problem 2136

ODE	\[ \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y=0} \]
program solution	\[ y = {\mathrm e}^{\frac {5 x}{2}} c_{1} +{\mathrm e}^{\left (-\frac {1}{2}-\frac {i \sqrt {31}}{2}\right ) x} c_{2} +{\mathrm e}^{\left (-\frac {1}{2}+\frac {i \sqrt {31}}{2}\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {31}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {31}\, x}{2}\right ) \]

Problem 2137

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} x \,{\mathrm e}^{2 x}+{\mathrm e}^{\left (-\frac {1}{2}-\frac {i \sqrt {15}}{2}\right ) x} c_{3} +{\mathrm e}^{\left (-\frac {1}{2}+\frac {i \sqrt {15}}{2}\right ) x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{4} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right )+{\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right ) \]

Problem 2138

ODE	\[ \boxed {4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y=0} \]
program solution	\[ y = {\mathrm e}^{\left (\frac {1}{4}-\frac {i \sqrt {15}}{4}\right ) x} c_{1} +{\mathrm e}^{\left (\frac {i \sqrt {15}}{4}+\frac {1}{4}\right ) x} c_{2} +{\mathrm e}^{-\frac {7 x}{2}} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {15 x}{4}} \sin \left (\frac {\sqrt {15}\, x}{4}\right )+c_{3} {\mathrm e}^{\frac {15 x}{4}} \cos \left (\frac {\sqrt {15}\, x}{4}\right )+c_{1} \right ) {\mathrm e}^{-\frac {7 x}{2}} \]

Problem 2139

ODE	\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{-i \sqrt {2}\, x} c_{2} +{\mathrm e}^{i \sqrt {2}\, x} c_{3} +{\mathrm e}^{-2 i x} c_{4} +{\mathrm e}^{2 i x} c_{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} \sin \left (\sqrt {2}\, x \right )+c_{3} \cos \left (\sqrt {2}\, x \right )+c_{4} \sin \left (2 x \right )+c_{5} \cos \left (2 x \right ) \]

Problem 2140

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

Problem 2141

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

Problem 2142

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

Problem 2143

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

Problem 2144

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

Problem 2145

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

Problem 2146

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

Problem 2147

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

Problem 2148

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

Problem 2149

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

Problem 2150

ODE	\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=x^{3}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-2 x}+\frac {c_{2} {\mathrm e}^{3 x}}{5}-\frac {x^{3}}{6}+\frac {x^{2}}{12}-\frac {7 x}{36}+\frac {13}{216} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}-\frac {1}{2} x^{2}+\frac {7}{6} x -\frac {13}{36}\right ) {\mathrm e}^{2 x}-6 c_{2} {\mathrm e}^{5 x}-6 c_{1} \right )}{6} \]

Problem 2151

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

Problem 2152

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

Problem 2153

ODE	\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }=x^{2}+8} \]
program solution	\[ y = c_{2} x +c_{1} +{\mathrm e}^{4 x} c_{3} -\frac {x^{4}}{48}-\frac {x^{3}}{48}-\frac {65 x^{2}}{64} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {65 x^{2}}{64}-\frac {x^{3}}{48}-\frac {x^{4}}{48}+\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_{2} x +c_{3} \]

Problem 2154

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

Problem 2155

ODE	\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y=x +{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{-2 i x} c_{2} +{\mathrm e}^{2 i x} c_{3} -\frac {{\mathrm e}^{2 x}}{8}-\frac {1}{36}-\frac {x}{12} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (936 c_{1} +18\right ) \cos \left (2 x \right )}{936}+\frac {\left (936 c_{3} +27\right ) \sin \left (2 x \right )}{936}+c_{2} {\mathrm e}^{3 x}-\frac {x}{12}-\frac {{\mathrm e}^{2 x}}{8}-\frac {1}{36} \]

Problem 2156

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

Problem 2157

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y={\mathrm e}^{2 x} x^{3}} \]
program solution	\[ y = {\mathrm e}^{-2 x} \left (c_{2} x +c_{1} \right )+\frac {9 x \,{\mathrm e}^{2 x}}{128}-\frac {3 x^{2} {\mathrm e}^{2 x}}{32}+\frac {{\mathrm e}^{2 x} x^{3}}{16}-\frac {3 \,{\mathrm e}^{2 x}}{128} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (8 x^{3}-12 x^{2}+9 x -3\right ) {\mathrm e}^{2 x}}{128}+{\mathrm e}^{-2 x} \left (c_{1} x +c_{2} \right ) \]

Problem 2158

ODE	\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y=x \,{\mathrm e}^{2 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{-i x} c_{2} +{\mathrm e}^{i x} c_{3} -\frac {4 x \,{\mathrm e}^{2 x}}{25}+\frac {x^{2} {\mathrm e}^{2 x}}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (5 x^{2}+50 c_{3} -8 x \right ) {\mathrm e}^{2 x}}{50}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \]

Problem 2159

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

Problem 2160

ODE	\[ \boxed {y^{\prime \prime }+2 n y^{\prime }+n^{2} y=5 \cos \left (6 x \right )} \]
program solution	\[ y = {\mathrm e}^{-n x} \left (c_{2} x +c_{1} \right )+\frac {\left (5 n^{2}-180\right ) \cos \left (6 x \right )}{\left (n^{2}+36\right )^{2}}+\frac {60 n \sin \left (6 x \right )}{\left (n^{2}+36\right )^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (n^{2}+36\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-n x}+5 \cos \left (6 x \right ) n^{2}+60 \sin \left (6 x \right ) n -180 \cos \left (6 x \right )}{\left (n^{2}+36\right )^{2}} \]

Problem 2161

ODE	\[ \boxed {y^{\prime \prime }+9 y=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+\frac {\sin \left (x \right )}{16}+\frac {\cos \left (2 x \right )}{5}-\frac {\sin \left (5 x \right )}{32} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (x \right )}{16}-\frac {\sin \left (5 x \right )}{32} \]

Problem 2162

ODE	\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )} \]
program solution	\[ y = {\mathrm e}^{-2 x} \left (c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )\right )-\frac {{\mathrm e}^{-4 x}}{5}-\frac {8}{25}+\frac {2 x}{5}-\frac {8 \cos \left (2 x \right )}{65}+\frac {\sin \left (2 x \right )}{65} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{2} {\mathrm e}^{-2 x} \sin \left (x \right )+{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} +\frac {\sin \left (2 x \right )}{65}+\frac {2 x}{5}-\frac {8}{25}-\frac {8 \cos \left (2 x \right )}{65}-\frac {{\mathrm e}^{-4 x}}{5} \]

Problem 2163

ODE	\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right )} \]
program solution	\[ y = c_{2} x +c_{1} +{\mathrm e}^{-2 x} c_{3} -\frac {10 \cos \left (3 x \right )}{117}-\frac {5 \sin \left (3 x \right )}{39}+\frac {5 x^{2} {\mathrm e}^{-2 x}}{8}+\frac {x^{3} {\mathrm e}^{-2 x}}{6}+{\mathrm e}^{-2 x} x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (8 x^{3}+30 x^{2}+12 c_{1} +48 x +33\right ) {\mathrm e}^{-2 x}}{48}+c_{2} x +c_{3} -\frac {10 \cos \left (3 x \right )}{117}-\frac {5 \sin \left (3 x \right )}{39} \]

Problem 2164

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

Problem 2165

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+4 y=5 \sin \left (3 x \right ) {\mathrm e}^{2 x}} \]
program solution	\[ y = {\mathrm e}^{\left (-1-i\right ) x} c_{1} +{\mathrm e}^{\left (1+i\right ) x} c_{2} +{\mathrm e}^{\left (1-i\right ) x} c_{3} +{\mathrm e}^{\left (-1+i\right ) x} c_{4} +\frac {24 \,{\mathrm e}^{2 x} \cos \left (3 x \right )}{1105}-\frac {23 \sin \left (3 x \right ) {\mathrm e}^{2 x}}{1105} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{3} +c_{4} \sin \left (x \right )\right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \left (24 \cos \left (3 x \right )-23 \sin \left (3 x \right )\right )}{1105}+{\mathrm e}^{x} \left (\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \right ) \]

Problem 2166

ODE	\[ \boxed {y^{\prime \prime }-5 y^{\prime }-6 y={\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ y = \frac {10 \,{\mathrm e}^{6 x}}{21}+\frac {45 \,{\mathrm e}^{-x}}{28}-\frac {{\mathrm e}^{3 x}}{12} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {10 \,{\mathrm e}^{6 x}}{21}+\frac {45 \,{\mathrm e}^{-x}}{28}-\frac {{\mathrm e}^{3 x}}{12} \]

Problem 2167

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

Problem 2168

ODE	\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=x \,{\mathrm e}^{-x}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{9}}, y^{\prime }\left (0\right ) = 0\right ] \end {align*}
program solution	\[ y = \frac {\left (6 x +5\right ) {\mathrm e}^{-x}}{36}-\frac {{\mathrm e}^{x}}{36} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (6 x +5\right ) {\mathrm e}^{-x}}{36}-\frac {{\mathrm e}^{x}}{36} \]

Problem 2169

ODE	\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right ) {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 2] \end {align*}
program solution	\[ y = \frac {\left (-2 \,{\mathrm e}^{x}+17\right ) \cos \left (x \right )}{5}+\frac {\sin \left (x \right ) \left ({\mathrm e}^{x}+11\right )}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-2 \,{\mathrm e}^{x}+17\right ) \cos \left (x \right )}{5}+\frac {\sin \left (x \right ) \left ({\mathrm e}^{x}+11\right )}{5} \]

Problem 2170

ODE	\[ \boxed {2 y^{\prime \prime }+y^{\prime }=8 \sin \left (2 x \right )+{\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = -\frac {\left (16 \,{\mathrm e}^{x} \sin \left (2 x \right )+4 \,{\mathrm e}^{x} \cos \left (2 x \right )-17-102 \,{\mathrm e}^{x}+98 \,{\mathrm e}^{\frac {x}{2}}\right ) {\mathrm e}^{-x}}{17} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {98 \,{\mathrm e}^{-\frac {x}{2}}}{17}-\frac {16 \sin \left (2 x \right )}{17}+{\mathrm e}^{-x}-\frac {4 \cos \left (2 x \right )}{17}+6 \]

Problem 2171

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

Problem 2172

ODE	\[ \boxed {2 y^{\prime \prime }+5 y^{\prime }-3 y=\sin \left (x \right )-8 x} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
program solution	\[ y = \frac {40}{9}-\frac {136 \,{\mathrm e}^{\frac {x}{2}}}{35}+\frac {13 \,{\mathrm e}^{-3 x}}{315}+\frac {8 x}{3}-\frac {\cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {8 \,{\mathrm e}^{-3 x} \left (-\frac {51 \,{\mathrm e}^{\frac {7 x}{2}}}{35}+\frac {13}{840}+\left (x -\frac {3 \cos \left (x \right )}{80}-\frac {3 \sin \left (x \right )}{80}+\frac {5}{3}\right ) {\mathrm e}^{3 x}\right )}{3} \]

Problem 2173

ODE	\[ \boxed {8 y^{\prime \prime }-y=x \,{\mathrm e}^{-\frac {x}{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
program solution	\[ y = \frac {\left (-5-16 \sqrt {2}\right ) {\mathrm e}^{-\frac {\sqrt {2}\, x}{4}}}{2}+\frac {\left (-5+16 \sqrt {2}\right ) {\mathrm e}^{\frac {\sqrt {2}\, x}{4}}}{2}+{\mathrm e}^{-\frac {x}{2}} \left (x +8\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-5-16 \sqrt {2}\right ) {\mathrm e}^{-\frac {\sqrt {2}\, x}{4}}}{2}+\frac {\left (-5+16 \sqrt {2}\right ) {\mathrm e}^{\frac {\sqrt {2}\, x}{4}}}{2}+\left (x +8\right ) {\mathrm e}^{-\frac {x}{2}} \]

Problem 2174

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

Problem 2175

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

Problem 2176

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

Problem 2177

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

Problem 2178

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

Problem 2179

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

Problem 2180

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

Problem 2181

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

Problem 2182

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }=\cos \left (2 x \right )} \]
program solution	\[ y = c_{2} {\mathrm e}^{x}+c_{1} +{\mathrm e}^{-4 x} c_{3} -\frac {3 \cos \left (2 x \right )}{100}-\frac {\sin \left (2 x \right )}{25} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-4 x} \left (\left (c_{3} -\frac {3 \cos \left (2 x \right )}{100}-\frac {\sin \left (2 x \right )}{25}-\frac {3}{100}\right ) {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{5 x}-\frac {c_{2}}{4}\right ) \]

Problem 2183

ODE	\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }={\mathrm e}^{3 x}} \]
program solution	\[ y = c_{2} {\mathrm e}^{x}+c_{1} +{\mathrm e}^{-5 x} c_{3} +\frac {{\mathrm e}^{3 x}}{48} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {{\mathrm e}^{-5 x} \left (-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{3} {\mathrm e}^{5 x}+c_{1} -\frac {5 \,{\mathrm e}^{8 x}}{48}\right )}{5} \]

Problem 2184

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

Problem 2185

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

Problem 2186

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

Problem 2187

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

Problem 2188

ODE	\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }={\mathrm e}^{2 x}+\sin \left (x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} +{\mathrm e}^{4 x} c_{3} -\frac {{\mathrm e}^{2 x}}{12}+\frac {5 \cos \left (x \right )}{34}+\frac {3 \sin \left (x \right )}{34} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{2} {\mathrm e}^{4 x}}{4}-{\mathrm e}^{-x} c_{1} +\frac {3 \sin \left (x \right )}{34}-\frac {{\mathrm e}^{2 x}}{12}+\frac {5 \cos \left (x \right )}{34}+c_{3} \]

Problem 2189

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

Problem 2190

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

Problem 2191

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

Problem 2192

ODE	\[ \boxed {y^{\prime \prime }-2 y={\mathrm e}^{-x} \sin \left (2 x \right )} \]
program solution	\[ y = c_{1} {\mathrm e}^{-\sqrt {2}\, x}+\frac {c_{2} \sqrt {2}\, {\mathrm e}^{\sqrt {2}\, x}}{4}+\frac {4 \,{\mathrm e}^{-x} \cos \left (2 x \right )}{41}-\frac {5 \,{\mathrm e}^{-x} \sin \left (2 x \right )}{41} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{-\sqrt {2}\, x} c_{1} +c_{2} {\mathrm e}^{\sqrt {2}\, x}+\frac {4 \,{\mathrm e}^{-x} \left (\cos \left (2 x \right )-\frac {5 \sin \left (2 x \right )}{4}\right )}{41} \]

Problem 2193

ODE	\[ \boxed {y^{\prime \prime }+9 y=\sec \left (x \right ) \csc \left (x \right )} \]
program solution	\[ y = c_{1} \cos \left (3 x \right )+\frac {c_{2} \sin \left (3 x \right )}{3}+\left (-\frac {4 \sin \left (x \right )}{3}+\frac {\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{3}\right ) \cos \left (3 x \right )+\left (\frac {4 \cos \left (x \right )}{3}+\frac {4 \ln \left (\csc \left (x \right )-\cot \left (x \right )\right )}{3}+\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )\right ) \sin \left (3 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sin \left (x \right ) \left (-1+4 \cos \left (x \right )^{2}\right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right )}{3}+\frac {\left (4 \cos \left (x \right )^{3}-3 \cos \left (x \right )\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{3}+4 c_{1} \cos \left (x \right )^{3}+4 \cos \left (x \right )^{2} \sin \left (x \right ) c_{2} +\frac {\left (-9 c_{1} +8 \sin \left (x \right )\right ) \cos \left (x \right )}{3}-\sin \left (x \right ) c_{2} \]

Problem 2194

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

Problem 2195

ODE	\[ \boxed {y^{\prime \prime }+y=\tan \left (\frac {x}{3}\right )^{2}} \]
program solution	\[ y = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )-22+9 \sin \left (\frac {x}{3}\right ) \left (-4 \cos \left (\frac {x}{3}\right )^{2}+1\right ) \ln \left (\sec \left (\frac {x}{3}\right )+\tan \left (\frac {x}{3}\right )\right )+36 \cos \left (\frac {x}{3}\right )^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -22+9 \sin \left (\frac {x}{3}\right ) \left (1-4 \cos \left (\frac {x}{3}\right )^{2}\right ) \ln \left (\sec \left (\frac {x}{3}\right )+\tan \left (\frac {x}{3}\right )\right )+36 \cos \left (\frac {x}{3}\right )^{2} \]

Problem 2196

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

Problem 2197

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

Problem 2198

ODE	\[ \boxed {y^{\prime }+P \left (x \right ) y=Q \left (x \right )} \]
program solution	\[ \int _{}^{x}\left (P \left (\textit {\_a} \right ) y-Q \left (\textit {\_a} \right )\right ) {\mathrm e}^{\int P \left (\textit {\_a} \right )d \textit {\_a}}d \textit {\_a} +\left (-{\mathrm e}^{\int _{}^{x}P \left (\textit {\_a} \right )d \textit {\_a}}+{\mathrm e}^{\int P \left (x \right )d x}\right ) y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\int Q \left (x \right ) {\mathrm e}^{\int P \left (x \right )d x}d x +c_{1} \right ) {\mathrm e}^{-\left (\int P \left (x \right )d x \right )} \]

Problem 2199

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

Problem 2200

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