\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = {\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \]

\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{-2 x} \left (1-15 x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{x} \left (7+6 x \right ) \]

\[ {}2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (17+30 x \right ) \]

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = 2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \]

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y = 2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \]

\[ {}8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y = {\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y = -3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \]

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y = -3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime } = -16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \]

\[ {}4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y = -{\mathrm e}^{x} \left (1-6 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y = {\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \]

\[ {}2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y = 18 \,{\mathrm e}^{x} \left (5+2 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y = -{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \]

\[ {}2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y = 3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \]

\[ {}2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (11+12 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \]

\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = {\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = -{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y = 8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y = {\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y = -{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime } = -{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = {\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y = {\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y = {\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (5+x \right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y = -{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y = {\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y = {\mathrm e}^{2 x} \left (-\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y = {\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (3 x +1\right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime } = -2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y = 10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (1+x \right ) \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (1+x \right )+{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime \prime \prime }+4 y = \sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (4-8 x \right ) \]

\[ {}4 y^{\prime \prime \prime }-3 y^{\prime }-y = {\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right ) \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \]

\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \]

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2} \]

\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{\frac {5}{2}} \]

\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \]

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \]

\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \]

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \]

\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \]

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \left (1+x \right ) \]

\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \]

\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \]

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right ) \]

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right ) \]

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \]

\[ {}[y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )] \]

\[ {}\left [y_{1}^{\prime }\left (t \right ) = -\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4}, y_{2}^{\prime }\left (t \right ) = \frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4}\right ] \]

\[ {}\left [y_{1}^{\prime }\left (t \right ) = -\frac {4 y_{1} \left (t \right )}{5}+\frac {3 y_{2} \left (t \right )}{5}, y_{2}^{\prime }\left (t \right ) = -\frac {2 y_{1} \left (t \right )}{5}-\frac {11 y_{2} \left (t \right )}{5}\right ] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right )] \]