2022 SAJC J2 BT Q1 [Modified]

The variables \(x\) and \(y\) are connected by the differential equation

\(\left( 2-x \right)\frac{\mathrm{d}y}{\mathrm{d}x}=x-y\), \(x < 2\).

1. Show that the substitution \(y=\left( 2-x \right)u\) reduces the differential equation to \(\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{x}{{{\left( 2-x \right)}^{2}}}\).[2]
2. Hence obtain the particular solution for which the solution curve passes through the origin.[4]