What is the solution for y^{''}+9y=cos(7t) ?

The solution for y^{''}+9y=cos(7t) is y=c_{1}cos(3t)+c_{2}sin(3t)-1/40 cos(7t)

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y^{''}+9y=cos(7t)

y^{^{''}} + 9 y = cos (7 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{1}{40} cos (7 t)

Solution steps

y^{''} (t) + 9 y = cos (7 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{1}{40} cos (7 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{1}{40} cos (7 t)

(D^{2} + 3 D - 10) y = 20 + 5 e^{3 x}

(D^{4} + 4 D^{2}) y = sin (2 x) + x e^{x} + 4

y^{^{''}} + 5 \frac{d y}{d x} - 6 y = 2 + (- 2) sin (2 x)

y^{^{''}} - y^{^{'}} + 6 y = 3 sin (2 x) + 4 cos (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}+9y=cos(7t) ?
The solution for y^{''}+9y=cos(7t) is y=c_{1}cos(3t)+c_{2}sin(3t)-1/40 cos(7t)