What is the solution for y^{''}+64y= 32/3 cos(7t) ?

The solution for y^{''}+64y= 32/3 cos(7t) is y=c_{1}cos(8t)+c_{2}sin(8t)+32/45 cos(7t)

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y^{''}+64y= 32/3 cos(7t)

y^{^{''}} + 64 y = \frac{32}{3} cos (7 t)

y = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{32}{45} cos (7 t)

Solution steps

y^{''} (t) + 64 y = \frac{32}{3} cos (7 t)

Solve linear ODE:

y = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{32}{45} cos (7 t)

y = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{32}{45} cos (7 t)

3 - x^{2}, 7 - 5 x

f (x) = 2 x^{2} + 3 x - 2, at x = - 2

\frac{x}{1 + x ^{2}}, at x = 2

\frac{d}{d x} (arctan (e^{- 2 x}))

6 x - 2, x^{2} + 2 x + 2, 1

What is the solution for y^{''}+64y= 32/3 cos(7t) ?
The solution for y^{''}+64y= 32/3 cos(7t) is y=c_{1}cos(8t)+c_{2}sin(8t)+32/45 cos(7t)