What is the solution for y^{''}+y^'=e^{5x} ?

The solution for y^{''}+y^'=e^{5x} is y=c_{1}+c_{2}e^{-x}+1/30 e^{5x}

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y^{''}+y^'=e^{5x}

y^{^{''}} + y^{^{'}} = e^{5 x}

y = c_{1} + c_{2} e^{- x} + \frac{1}{30} e^{5 x}

Solution steps

y^{''} (x) + y^{'} (x) = e^{5 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{1}{30} e^{5 x}

y = c_{1} + c_{2} e^{- x} + \frac{1}{30} e^{5 x}

y^{^{''}} - 16 y^{^{'}} + 64 y = 6 e^{8 x}

y^{^{''}} - 4 y^{^{'}} + 3 y = sin (e^{- x})

y^{^{''}} + 2 y^{^{'}} + y = x ln (x)

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

y^{^{''}} - 7 y^{^{'}} + 10 y = 2 x e^{x}

What is the solution for y^{''}+y^'=e^{5x} ?
The solution for y^{''}+y^'=e^{5x} is y=c_{1}+c_{2}e^{-x}+1/30 e^{5x}