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}

(d^{2} + 1) y = x^{2} e^{3} x

4 y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- 3} x + 18 x + 15

(d^{5} - d) y = 12 e^{x} + 8 sin (x) - 2 x

(d^{3} - 3 d^{2} + 3 d - 1) y = 4 cos (x)

y^{^{''}} + 4 y^{^{'}} = 8 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