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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 4 x = 2 e^{t}

y^{^{'''}} + y = 4 e^{x}

y^{^{''}} + 4 y = 2 e^{- x}

y^{^{''}} + 2 y^{^{'}} + 10 y = 50 x, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} = \frac{10 sin ( 7 t )}{2}

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