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

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

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(d^2-1)y=e^x

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

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

Solution steps

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

Solve linear ODE:

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

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

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