What is the solution for y^{''}=y+e^{2x}e^{e^x} ?

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

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

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

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

Solution steps

y^{''} (x) = y + e^{2 x} e^{e^{x}}

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} = t^{2} + 2 e^{t}

y^{^{'}} + y^{^{''}} + y = x e^{x}

y^{^{''}} + 2 y^{^{'}} - 15 y = (2 x + 1) e^{3 x} + 10

y^{^{''}} - y^{^{'}} - 2 y = 2 t^{2} - 5

y^{^{''}} - 3 y^{^{'}} - 4 y = 2^{t - 2}, y (2) = 1, y^{^{'}} (2) = - 1

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