What is the solution for y^{''}+4y^'=3sin(2t) ?

The solution for y^{''}+4y^'=3sin(2t) is y=c_{1}+c_{2}e^{-4t}-3/20 sin(2t)-3/10 cos(2t)

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y^{''}+4y^'=3sin(2t)

y^{^{''}} + 4 y^{^{'}} = 3 sin (2 t)

y = c_{1} + c_{2} e^{- 4 t} - \frac{3}{20} sin (2 t) - \frac{3}{10} cos (2 t)

Solution steps

y^{''} (t) + 4 y^{'} (t) = 3 sin (2 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} - \frac{3}{20} sin (2 t) - \frac{3}{10} cos (2 t)

y = c_{1} + c_{2} e^{- 4 t} - \frac{3}{20} sin (2 t) - \frac{3}{10} cos (2 t)

What is the solution for y^{''}+4y^'=3sin(2t) ?
The solution for y^{''}+4y^'=3sin(2t) is y=c_{1}+c_{2}e^{-4t}-3/20 sin(2t)-3/10 cos(2t)