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

The solution for y^{''}+16y=-32sec(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-2ln(cos(4t))cos(4t)-8tsin(4t)

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

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 2 ln (cos (4 t)) cos (4 t) - 8 t sin (4 t)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 2 ln (cos (4 t)) cos (4 t) - 8 t sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 2 ln (cos (4 t)) cos (4 t) - 8 t sin (4 t)

\int 3 y^{2} - 2 x d y

\frac{d}{d x} (ln (ln (2 x^{4})))

\int \frac{4 x}{x ^{4} - 12 x ^{2} + 45} d x

f (x) = 4 x^{2}, at x = 1

\frac{\partial}{\partial x} (x^{9 y})

What is the solution for y^{''}+16y=-32sec(4t) ?
The solution for y^{''}+16y=-32sec(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-2ln(cos(4t))cos(4t)-8tsin(4t)