What is the solution for y^{''}-4y=24cos(2t) ?

The solution for y^{''}-4y=24cos(2t) is y=c_{1}e^{2t}+c_{2}e^{-2t}-3cos(2t)

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y^{''}-4y=24cos(2t)

y^{^{''}} - 4 y = 24 cos (2 t)

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3 cos (2 t)

Solution steps

y^{''} (t) - 4 y = 24 cos (2 t)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3 cos (2 t)

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 3 cos (2 t)

y^{^{''}} + 2 y^{^{'}} + 10 y = 2 cos (x) + cos (3 x)

y^{^{''}} + 100 y^{^{'}} + 2500 y = 20

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

y^{^{''}} - 4 y^{^{'}} - y - 2 = 0

x^{^{''}} + 4 x = 10 cos (3 t)

What is the solution for y^{''}-4y=24cos(2t) ?
The solution for y^{''}-4y=24cos(2t) is y=c_{1}e^{2t}+c_{2}e^{-2t}-3cos(2t)