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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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