First, we note that we cannot separate the variables so that the x expressions are with dx only and the y expressions are with dy only. So the DE is not separable.

So we aim to get the DE in one of the integrable combination forms. Rearranging, we have:

2y dy + (x dy + y dx) = 0

From the integrable combination (1) given above, the expression in brackets can be written as d(xy) and the differential equation is equivalent to:

2y dy + d(xy) = 0

Integrating gives us:

y² + xy = K (General Solution)

CHECK (using Implicit Differentiation):

So on multiplying by dx throughout, we have:

2y dy + x dy + y dx = 0

which is the DE that we started with so we know our general solution is correct.