Linear First Order ODE/x y' + y = x^2 cosine x/Proof 1

Proof
Rearranging:
 * $\dfrac {\d y} {\d x} + \dfrac y x = x \cos x$

This is in the form:
 * $\dfrac {\d y} {\d x} + \map P x y = \map Q x$

where:
 * $\map P x = \dfrac 1 x$
 * $\map Q x = x \cos x$

Thus:

Thus from Solution by Integrating Factor:
 * $\map {\dfrac {\d} {\d x} } {x y} = x^2 \cos x$