What is the solution for 2y^{''}+6y^'=10sin(7t) ?

The solution for 2y^{''}+6y^'=10sin(7t) is y=c_{1}+c_{2}e^{-3t}-5/58 sin(7t)-15/406 cos(7t)

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2y^{''}+6y^'=10sin(7t)

2 y^{^{''}} + 6 y^{^{'}} = 10 sin (7 t)

y = c_{1} + c_{2} e^{- 3 t} - \frac{5}{58} sin (7 t) - \frac{15}{406} cos (7 t)

Solution steps

2 y^{''} (t) + 6 y^{'} (t) = 10 sin (7 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 t} - \frac{5}{58} sin (7 t) - \frac{15}{406} cos (7 t)

y = c_{1} + c_{2} e^{- 3 t} - \frac{5}{58} sin (7 t) - \frac{15}{406} cos (7 t)

What is the solution for 2y^{''}+6y^'=10sin(7t) ?
The solution for 2y^{''}+6y^'=10sin(7t) is y=c_{1}+c_{2}e^{-3t}-5/58 sin(7t)-15/406 cos(7t)