What is the solution for y^{''}+5y^'-6y=22+18x-18x^2 ?

The solution for y^{''}+5y^'-6y=22+18x-18x^2 is y=c_{1}e^x+c_{2}e^{-6x}+3x^2+2x-1

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y^{''}+5y^'-6y=22+18x-18x^2

y^{^{''}} + 5 y^{^{'}} - 6 y = 22 + 18 x - 18 x^{2}

y = c_{1} e^{x} + c_{2} e^{- 6 x} + 3 x^{2} + 2 x - 1

Solution steps

y^{''} (x) + 5 y^{'} (x) - 6 y = 22 + 18 x - 18 x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} + 3 x^{2} + 2 x - 1

y = c_{1} e^{x} + c_{2} e^{- 6 x} + 3 x^{2} + 2 x - 1

\frac{d}{d x} (f (x) (4 sin (x^{2} - 1)))

\int x^{2} x^{2} - 49 d x

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

\int_{0.2}^{0.4} 200 x d x

\int \frac{6}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

What is the solution for y^{''}+5y^'-6y=22+18x-18x^2 ?
The solution for y^{''}+5y^'-6y=22+18x-18x^2 is y=c_{1}e^x+c_{2}e^{-6x}+3x^2+2x-1