What is the solution for x^{''}+9x=5sin(3t) ?

The solution for x^{''}+9x=5sin(3t) is x=c_{1}cos(3t)+c_{2}sin(3t)-(5tcos(3t))/6

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x^{''}+9x=5sin(3t)

x^{^{''}} + 9 x = 5 sin (3 t)

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{5 t cos ( 3 t )}{6}

Solution steps

x^{''} (t) + 9 x = 5 sin (3 t)

Solve linear ODE:

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{5 t cos ( 3 t )}{6}

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{5 t cos ( 3 t )}{6}

y^{^{''}} - 4 y = (x^{2} - 7) sin (2 x)

y^{^{''}} - 36 y = sinh (6 x)

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

y^{^{''}} - y^{^{'}} + y = \frac{sin ( t )}{3} - 2 e^{2 t}

x^{^{''}} + 4 x^{^{'}} + 29 = 0

What is the solution for x^{''}+9x=5sin(3t) ?
The solution for x^{''}+9x=5sin(3t) is x=c_{1}cos(3t)+c_{2}sin(3t)-(5tcos(3t))/6