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}

y^{^{''}} + \frac{53}{7} \cdot y^{^{'}} + 49 x = 0

2 y^{^{''}} - 18 y^{^{'}} = 6 tan (3 x)

D (f (x)) = 4 sec (4 x) tan (4) (x)

2 y^{^{''}} + 9 y^{^{'}} + 9 y = 2 x

y^{^{''}} - 8 y + 16 y = t^{- 3} e^{4 t}

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