First order differential equations (integrating factor)
Given the differential equation
$$\cos x \frac { \mathrm {~d} y } { \mathrm {~d} x } + y \sin x = 4 \cos ^ { 3 } x \sin x + 5$$
and \(y = 3 \sqrt { 2 }\) when \(x = \frac { \pi } { 4 }\), find an equation for \(y\) in terms of \(x\).
□