What is the solution for (d^2+d-6)y=e^{-3}x ?

The solution for (d^2+d-6)y=e^{-3}x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/(6e^3)-1/(36e^3)

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(d^2+d-6)y=e^{-3}x

(d^{2} + d - 6) y = e^{- 3} x

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6 e ^{3}} - \frac{1}{36 e ^{3}}

Solution steps

(d^{2} + d - 6) y = e^{- 3} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6 e ^{3}} - \frac{1}{36 e ^{3}}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6 e ^{3}} - \frac{1}{36 e ^{3}}

y^{^{'''}} - 5 y^{^{''}} = 2 x

y^{^{''}} - 2 y^{^{'}} - 3 y = e t, y (0) = 2, y^{^{'}} (0) = 4

x^{^{''}} + 23.04 x = 2 cos (5 t)

y^{^{''}} + 4 y = 9, t y (0) = 0, y^{^{'}} (0) = 7

y^{^{''}} + 8 y^{^{'}} + 12 y = 1 - H (t)

What is the solution for (d^2+d-6)y=e^{-3}x ?
The solution for (d^2+d-6)y=e^{-3}x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/(6e^3)-1/(36e^3)