What is the solution for y^{''}-y=2e^x+6e^{2x} ?

The solution for y^{''}-y=2e^x+6e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+e^xx+2e^{2x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}-y=2e^x+6e^{2x} ?
The solution for y^{''}-y=2e^x+6e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+e^xx+2e^{2x}