What is the solution for y^{''}+2y^'+y=e^3+e^{2x} ?

The solution for y^{''}+2y^'+y=e^3+e^{2x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+e^3+1/9 e^{2x}

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y^{''}+2y^'+y=e^3+e^{2x}

y^{^{''}} + 2 y^{^{'}} + y = e^{3} + e^{2 x}

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{3} + \frac{1}{9} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{3} + \frac{1}{9} e^{2 x}

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{3} + \frac{1}{9} e^{2 x}

y^{^{''}} + y^{^{'}} + 12 y = 20 cos (3 t)

y^{^{''}} - 9 y = sin (x)

\frac{d ^{2} u}{d y ^{2}} - 4 u + 6 = 0

y^{^{''}} - 16 y = 32 + 45 e^{x}, y (0) = 0

y^{^{'''}} - 81 y^{^{'}} = t e^{- 9 t} + 10 cos (9 t)

What is the solution for y^{''}+2y^'+y=e^3+e^{2x} ?
The solution for y^{''}+2y^'+y=e^3+e^{2x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+e^3+1/9 e^{2x}