Solve the following initial value problem using the method of separation of variables:

$(2yx)\frac{dy}{dx}=y$

with the initial condition $y(1)=2.$

Instructions

$($a$)$ Rearrange the equation into the form $f(y,x)dy=g(y,x)dx.$

Hint: Factor out $y$ on the right$-$hand side to help with separation.

$($b$)$ Integrate both sides and express the general solution.

$($c$)$ Apply the initial condition to find the particular solution.