What is the solution for (D^3-D)y=4e^{(-x)}+3e^2x ?

The solution for (D^3-D)y=4e^{(-x)}+3e^2x is y=c_{1}+c_{2}e^{-x}+c_{3}e^x+2xe^{-x}-(3e^2x^2)/2

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(D^3-D)y=4e^{(-x)}+3e^2x

(D^{3} - D) y = 4 e^{(- x)} + 3 e^{2} x

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

Solution steps

(D^{3} - D) y = 4 e^{- x} + 3 e^{2} x

Solve linear ODE:

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

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

y^{^{''}} + 36 y = 60 sin (6 t)

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 2 x = 2

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - y = x sinh (x)

y^{^{''}} + y = sin (x)

y^{^{'''}} + 12 y^{^{''}} + 48 y^{^{'}} + 64 y = 4 e^{- 4 x}

What is the solution for (D^3-D)y=4e^{(-x)}+3e^2x ?
The solution for (D^3-D)y=4e^{(-x)}+3e^2x is y=c_{1}+c_{2}e^{-x}+c_{3}e^x+2xe^{-x}-(3e^2x^2)/2