What is the solution for (d^2-1)y=e^x+4e^{-x} ?

The solution for (d^2-1)y=e^x+4e^{-x} is y=c_{1}e^x+c_{2}e^{-x}+(e^xx)/2-2xe^{-x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y - 12 y = 2 sin (t)

y^{^{''}} + 4 y = 3 cos (2)

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{x} sin (2 x)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2} x, y (0) = 1, y^{^{'}} (0) = 3

8 y^{^{''}} - y^{^{'}} + y + x^{2} = 0

What is the solution for (d^2-1)y=e^x+4e^{-x} ?
The solution for (d^2-1)y=e^x+4e^{-x} is y=c_{1}e^x+c_{2}e^{-x}+(e^xx)/2-2xe^{-x}