What is the solution for y^{''}+3y^'=x^2+9 ?

The solution for y^{''}+3y^'=x^2+9 is y=c_{1}+c_{2}e^{-3x}+(x^3)/9-(x^2)/9+(83x)/(27)

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y^{''}+3y^'=x^2+9

y^{^{''}} + 3 y^{^{'}} = x^{2} + 9

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{83 x}{27}

Solution steps

y^{''} (x) + 3 y^{'} (x) = x^{2} + 9

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{83 x}{27}

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{83 x}{27}

y^{^{''}} + 9 y = 4 sec (3 x)

y^{^{''''}} + 20 y^{^{''}} + 100 = 0

x^{^{''}} - 4 x^{^{'}} + 4 x = 2 sin (2 t)

y^{^{''}} - 3 y^{^{'}} - 4 y = 1 - 8 x^{2} + 48 e^{- 4 x}

y^{^{'''}} + 15 y^{^{''}} - 500 y = e^{- 10 x}

What is the solution for y^{''}+3y^'=x^2+9 ?
The solution for y^{''}+3y^'=x^2+9 is y=c_{1}+c_{2}e^{-3x}+(x^3)/9-(x^2)/9+(83x)/(27)