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

The solution for 2y^{''}-y=4sin(3t) is y=c_{1}e^{t/(sqrt(2))}+c_{2}e^{-t/(sqrt(2))}-4/19 sin(3t)

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

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

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - \frac{4}{19} sin (3 t)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - \frac{4}{19} sin (3 t)

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - \frac{4}{19} sin (3 t)

What is the solution for 2y^{''}-y=4sin(3t) ?
The solution for 2y^{''}-y=4sin(3t) is y=c_{1}e^{t/(sqrt(2))}+c_{2}e^{-t/(sqrt(2))}-4/19 sin(3t)