What is the solution for y^{''}+y^'=5x+2e^x ?

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

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

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

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

Solution steps

y^{''} (x) + y^{'} (x) = 5 x + 2 e^{x}

Solve linear ODE:

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

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

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