What is the solution for y^{''}+3y^'+2y=13+ex ?

The solution for y^{''}+3y^'+2y=13+ex is y=c_{1}e^{-x}+c_{2}e^{-2x}+(ex)/2+(26-3e)/4

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y^{''}+3y^'+2y=13+ex

y^{^{''}} + 3 y^{^{'}} + 2 y = 13 + e x

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e x}{2} + \frac{26 - 3 e}{4}

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 13 + e x

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e x}{2} + \frac{26 - 3 e}{4}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e x}{2} + \frac{26 - 3 e}{4}

y^{^{''}} + 10 y^{^{'}} + 25 y = 30 x + 3

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

y^{^{''}} + 9 y = \frac{3}{2} sin (2 t)

y^{^{''}} - 2 y^{^{'}} - 8 y = 10 e^{3 x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 5 e^{- 2 x} - e^{- x}

What is the solution for y^{''}+3y^'+2y=13+ex ?
The solution for y^{''}+3y^'+2y=13+ex is y=c_{1}e^{-x}+c_{2}e^{-2x}+(ex)/2+(26-3e)/4