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

The solution for y^{''}-4y=4e^x is y=c_{1}e^{2x}+c_{2}e^{-2x}-4/3 e^x

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{4}{3} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{4}{3} e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{4}{3} e^{x}

y^{^{''}} + 4 y = g (x), y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} + 4 y^{^{'}} - 5 y = 10 x^{2} + 9 e^{x}

(d - 1)^{2} (d - 3)^{3} y = e^{3} x

y^{^{''}} - 2 y^{^{'}} - 3 y = 15 t e^{2 t}

y^{^{''}} = 3 cos (t) - 2 y

What is the solution for y^{''}-4y=4e^x ?
The solution for y^{''}-4y=4e^x is y=c_{1}e^{2x}+c_{2}e^{-2x}-4/3 e^x