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)

\frac{d}{d x} (\frac{2}{3} x + \frac{4}{3 x ^{2}})

\frac{d}{d x} (f (x) \circ g (x))

x \to 1 - lim (\frac{x ^{3} - 1}{x - 1})

(x - 7)^{4} y^{^{'}} + 5 (x - 7)^{3} y = x + 7

\int \frac{1}{tan ( y )} d y

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)