What is the solution for y^{''}+5y^'+6y=108x^2 ?

The solution for y^{''}+5y^'+6y=108x^2 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+18x^2-30x+19

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y^{''}+5y^'+6y=108x^2

y^{^{''}} + 5 y^{^{'}} + 6 y = 108 x^{2}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + 18 x^{2} - 30 x + 19

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = 108 x^{2}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + 18 x^{2} - 30 x + 19

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + 18 x^{2} - 30 x + 19

\int_{7}^{\infty} \frac{ln ( x )}{x} d x

\int_{1}^{2} (x^{2}) d x

\int 9 x^{- 3} d x

\frac{d}{d x} (\frac{2 x}{7 x ^{2} + 1})

What is the solution for y^{''}+5y^'+6y=108x^2 ?
The solution for y^{''}+5y^'+6y=108x^2 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+18x^2-30x+19