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

The solution for y^{''}+5y^'=x+2 is y=c_{1}+c_{2}e^{-5x}+(x^2)/(10)+(9x)/(25)

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

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

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} + \frac{9 x}{25}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} + \frac{9 x}{25}

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} + \frac{9 x}{25}

What is the solution for y^{''}+5y^'=x+2 ?
The solution for y^{''}+5y^'=x+2 is y=c_{1}+c_{2}e^{-5x}+(x^2)/(10)+(9x)/(25)