What is the solution for y^{''}-y=5sin(2t) ?

The solution for y^{''}-y=5sin(2t) is y=c_{1}e^t+c_{2}e^{-t}-sin(2t)

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y^{''}-y=5sin(2t)

y^{^{''}} - y = 5 sin (2 t)

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

Solution steps

y^{''} (t) - y = 5 sin (2 t)

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 6 y = 3 e^{2 t}

y^{^{''}} - 4 y = 6 x - 4 x^{3}

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 + 16 x

y^{^{''}} + y = 2 x \cdot sin (x)

What is the solution for y^{''}-y=5sin(2t) ?
The solution for y^{''}-y=5sin(2t) is y=c_{1}e^t+c_{2}e^{-t}-sin(2t)