What is the solution for y^{''}+36y=33cos(5x) ?

The solution for y^{''}+36y=33cos(5x) is y=c_{1}cos(6x)+c_{2}sin(6x)+3cos(5x)

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y^{''}+36y=33cos(5x)

y^{^{''}} + 36 y = 33 cos (5 x)

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

Solution steps

y^{''} (x) + 36 y = 33 cos (5 x)

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{'}} = 2 \cdot cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (2 t)

y^{^{''}} - 3 y^{^{'}} - 6 y = 2 t^{2} + 2 t - 5 e^{3 t}

d (x) = 2 x - 4

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

What is the solution for y^{''}+36y=33cos(5x) ?
The solution for y^{''}+36y=33cos(5x) is y=c_{1}cos(6x)+c_{2}sin(6x)+3cos(5x)