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

The solution for y^{''}+3y^'=x+3 is y=c_{1}+c_{2}e^{-3x}+(x^2)/6+(8x)/9

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

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

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{8 x}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{8 x}{9}

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{8 x}{9}

What is the solution for y^{''}+3y^'=x+3 ?
The solution for y^{''}+3y^'=x+3 is y=c_{1}+c_{2}e^{-3x}+(x^2)/6+(8x)/9