What is the solution for y^{''}-y=2(e^xe^{-x})^{-1} ?

The solution for y^{''}-y=2(e^xe^{-x})^{-1} is y=c_{1}e^x+c_{2}e^{-x}-2

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

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{''}} - y = x e^{\frac{1}{2} x}

y^{^{''}} + 2 y^{^{'}} + y = 3 cos (t)

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

x^{^{''}} + 4 x^{^{'}} + 5 x = e^{- 2} t sin (t)

d, d (t) = - 16 t^{2} + 32 t + 40

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