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} \cdot 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} \cdot 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^{^{''}} - 2 y^{^{'}} + 4 y = 2 x e^{2 x}

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 e^{x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{x} sin (x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 - 3 e^{x}

y^{^{''}} - y = 4 x^{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}