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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 5 (e^{x} + e^{3 x})

\frac{d ^{2}}{d x ^{2}} (θ (x)) - (a + b) θ (x) = (a \cdot c + b)

y^{^{''}} + 2 y^{^{'}} + y = e^{2 x} + cos (x)

y^{^{''}} + y - 1 = 0, y (0) = 0, y (1) = 0

y^{^{''}} - y^{^{'}} = 4 x e^{x}

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