What is the solution for x^{''}+36x=33cos(5t) ?

The solution for x^{''}+36x=33cos(5t) is x=c_{1}cos(6t)+c_{2}sin(6t)+3cos(5t)

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x^{''}+36x=33cos(5t)

x^{^{''}} + 36 x = 33 cos (5 t)

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

Solution steps

x^{''} (t) + 36 x = 33 cos (5 t)

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 y = 24

y^{^{''}} + y = 3 x sin (x)

x^{^{''}} + 6 x^{^{'}} + 25 x = t e^{- t}

y^{^{''}} + 9 y = 2 sec (3 x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- x} - sin (2 x)

What is the solution for x^{''}+36x=33cos(5t) ?
The solution for x^{''}+36x=33cos(5t) is x=c_{1}cos(6t)+c_{2}sin(6t)+3cos(5t)