What is the solution for y^{''}-4y=8sin(2x) ?

The solution for y^{''}-4y=8sin(2x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-sin(2x)

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y^{''}-4y=8sin(2x)

y^{^{''}} - 4 y = 8 sin (2 x)

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

Solution steps

y^{''} (x) - 4 y = 8 sin (2 x)

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} - 1 = 0

q^{^{''}} + 100 q^{^{'}} + 2500 q = 30, q (0) = 0, q (0) = 2

(D^{3} + D) y = e^{- 2 x} cos (2 x)

x^{^{''}} + 2.5 x^{^{'}} + 50 x = 1.5 cos (t)

y^{^{''}} + 4 y = g (t), y (0) = 6, y^{^{'}} (0) = 18

What is the solution for y^{''}-4y=8sin(2x) ?
The solution for y^{''}-4y=8sin(2x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-sin(2x)