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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

f (x) = ln (1)

\int x e^{(3 x)} d x

\int \frac{15}{4 + 5 x} d x

\int_{- 3}^{4} y - (y^{2} - 12) d y

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