What is the solution for (D^2-1)y=e^x+1 ?

The solution for (D^2-1)y=e^x+1 is y=c_{1}e^x+c_{2}e^{-x}+(e^xx)/2-1

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(D^2-1)y=e^x+1

(D^{2} - 1) y = e^{x} + 1

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

Solution steps

(D^{2} - 1) y = e^{x} + 1

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0

y^{^{''}} + y^{^{'}} + y = sin (t)

y^{^{''}} - 2 a y^{^{'}} + a^{2} y = ∣ t ∣

y^{^{''}} - 10 y^{^{'}} + 25 y = 2 e^{5} x

6 y^{^{''}} + y^{^{'}} - y = - 25 e^{2 x} + 7 e^{- 2 x}

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