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

The solution for y^{''}-y=e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+1/3 e^{2x}

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

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

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{1}{3} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{1}{3} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{1}{3} e^{2 x}

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

2 y^{^{''}} + y^{^{'}} - y = x + 7, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 6 e^{3 t} - 3 e^{- t}

y^{^{''}} + 2 y^{^{'}} - 24 y = 16 - (x + 2) e^{4 x}

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

What is the solution for y^{''}-y=e^{2x} ?
The solution for y^{''}-y=e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+1/3 e^{2x}