What is the solution for y^{''}+16y=-32sin(4t) ?

The solution for y^{''}+16y=-32sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)+4tcos(4t)

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y^{''}+16y=-32sin(4t)

y^{^{''}} + 16 y = - 32 sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 4 t cos (4 t)

Solution steps

y^{''} (t) + 16 y = - 32 sin (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 4 t cos (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 4 t cos (4 t)

3 arcsin (x^{3})

\frac{d v}{d t} = v^{2} + 5 v + 6

f (x) = x \cdot ln (x) - x

x \to 0 lim (x^{- 1} - 1)

y = 8 x - x^{2}, y = 0

What is the solution for y^{''}+16y=-32sin(4t) ?
The solution for y^{''}+16y=-32sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)+4tcos(4t)