What is the solution for (d^2y)/(dx^2)-4y=4e^{2x} ?

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

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(d^2y)/(dx^2)-4y=4e^{2x}

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 e^{2 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 sin (2 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 8 y = 4 e^{- 2 x}

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

y^{^{''}} + 2 y^{^{'}} + 10 y = x, y (0) = 0, y^{^{'}} (0) = - 1

y^{^{''}} + 17 y = e^{6 x}

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