What is the solution for y^{''}-4y=2e^{2x} ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 2 y = 1 + t

y^{^{'''}} + 25 y^{^{'}} = tan (5 x)

y^{^{''}} - 5 y^{^{'}} + 6 y = (x + 1)^{2} e^{2 x}

y^{^{''}} - 2 y^{^{'}} + 5 y = - 8

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

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