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

The solution for y^{''}+3y^'=x^2 is y=c_{1}+c_{2}e^{-3x}+(x^3)/9-(x^2)/9+(2x)/(27)

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

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

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

What is the solution for y^{''}+3y^'=x^2 ?
The solution for y^{''}+3y^'=x^2 is y=c_{1}+c_{2}e^{-3x}+(x^3)/9-(x^2)/9+(2x)/(27)