First order differential equations (integrating factor)
4
Use the substitution \(y = x z\) to find the general solution of the differential equation
$$x \frac { \mathrm {~d} y } { \mathrm {~d} x } - y = x \cos \left( \frac { y } { x } \right)$$
giving your answer in a form without logarithms. (You may quote an appropriate result given in the List of Formulae (MF1).)
Find the solution of the differential equation for which \(y = \pi\) when \(x = 4\).