What is the solution for y^{''}-2y-3y=x+2 ?

The solution for y^{''}-2y-3y=x+2 is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-x/5-2/5

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y^{''}-2y-3y=x+2

y^{^{''}} - 2 y - 3 y = x + 2

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x}{5} - \frac{2}{5}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x}{5} - \frac{2}{5}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x}{5} - \frac{2}{5}

y^{^{''}} - 12 y^{^{'}} + 37 y = e^{6 x} - x^{2}

(D^{2} + 4 D + 3) y = 2 x e^{3 x} + 3 e^{3 x} cos (2 x)

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{3 x} ln (x)

4 y^{^{''}} + 8 y^{^{'}} + 10 y = 4 cos (t)

What is the solution for y^{''}-2y-3y=x+2 ?
The solution for y^{''}-2y-3y=x+2 is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-x/5-2/5