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

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

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(d^2+3d+2)y=(e^e)^x

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3} x}{x}

(d^{3} + d^{2} - 4 d - 4) y = 3 e^{- x} - 4 x - 6

(d^{2} - 2 d + 4) \cdot y = e^{x} \cdot cos (x)

y^{^{'''}} - 3 y^{^{''}} - 10 y^{^{'}} + 24 = 2 x^{2} - 5

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

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