What is the solution for 3x^{''}+10x=2sin(3t) ?

The solution for 3x^{''}+10x=2sin(3t) is x=c_{1}cos(sqrt(10/3)t)+c_{2}sin(sqrt(10/3)t)-2/17 sin(3t)

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3x^{''}+10x=2sin(3t)

3 x^{^{''}} + 10 x = 2 sin (3 t)

x = c_{1} cos (\frac{10}{3} t) + c_{2} sin (\frac{10}{3} t) - \frac{2}{17} sin (3 t)

Solution steps

3 x^{''} (t) + 10 x = 2 sin (3 t)

Solve linear ODE:

x = c_{1} cos (\frac{10}{3} t) + c_{2} sin (\frac{10}{3} t) - \frac{2}{17} sin (3 t)

x = c_{1} cos (\frac{10}{3} t) + c_{2} sin (\frac{10}{3} t) - \frac{2}{17} sin (3 t)

What is the solution for 3x^{''}+10x=2sin(3t) ?
The solution for 3x^{''}+10x=2sin(3t) is x=c_{1}cos(sqrt(10/3)t)+c_{2}sin(sqrt(10/3)t)-2/17 sin(3t)