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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 0 lim (cot (x) arcsin (x))

\int \frac{1}{7 - 2 x} d x

\frac{d y}{d x} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

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

\frac{\partial}{\partial x} (x^{a} y^{b} z^{c})

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