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

The solution for y^{''}+y^'-2y=e^{2x} is y=c_{1}e^x+c_{2}e^{-2x}+1/4 e^{2x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 + e^{- x}

y^{^{''}} - 9 y = e^{3 x}, y (0) = 1, y^{^{'}} (0) = - 5

y^{^{''}} + y^{^{'}} - 6 y = e^{- 5 x} (- 102 + 146 x - 70 x^{2})

y^{^{''}} + 4 y = x e^{x} - e^{x} + 2 e^{3 x}

What is the solution for y^{''}+y^'-2y=e^{2x} ?
The solution for y^{''}+y^'-2y=e^{2x} is y=c_{1}e^x+c_{2}e^{-2x}+1/4 e^{2x}