What is the solution for (d^2y)/(dx^2)-4y=4sin(2x)-3e^2x ?

The solution for (d^2y)/(dx^2)-4y=4sin(2x)-3e^2x is y=c_{1}e^{2x}+c_{2}e^{-2x}-1/2 sin(2x)+(3e^2x)/4

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(d^2y)/(dx^2)-4y=4sin(2x)-3e^2x

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

Solve linear ODE:

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

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

12 y^{^{''}} - 5 y^{^{'}} - 3 y = e^{x}

y^{^{''}} + 4 y = sin (6 x)

y^{^{''}} - 2 y^{^{'}} + y = e^{t} + t, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2} x (cos (x) - 6 sin (x))

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

What is the solution for (d^2y)/(dx^2)-4y=4sin(2x)-3e^2x ?
The solution for (d^2y)/(dx^2)-4y=4sin(2x)-3e^2x is y=c_{1}e^{2x}+c_{2}e^{-2x}-1/2 sin(2x)+(3e^2x)/4