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

The solution for y^{''}+y^'-2y=x^2 is y=c_{1}e^x+c_{2}e^{-2x}-(x^2)/2-x/2-3/4

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{3}{4}

f (x) = \frac{9}{5 x}

\int (x - 7)^{3} d x

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

y^{^{''}} + 2 y^{^{'}} = 3 + 4 sin (2 x)

\frac{d}{d x} (1 - 3 x^{2})

What is the solution for y^{''}+y^'-2y=x^2 ?
The solution for y^{''}+y^'-2y=x^2 is y=c_{1}e^x+c_{2}e^{-2x}-(x^2)/2-x/2-3/4