What is the solution for y^{''}-y^'-2y=1-x ?

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

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y^{''}-y^'-2y=1-x

y^{^{''}} - y^{^{'}} - 2 y = 1 - x

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

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 1 - x

Solve linear ODE:

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

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

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