Solving the differential equation $7x(x-y)dy = 2(x^2+6xy-5y^2)dx$ How do I solve the differential equation $$7x(x-y)dy = 2(x^2+6xy-5y^2)dx$$
Is it homogeneous? I have tried taking the variables from the LHS and applying them to the RHS, making $\frac{dy}{dx}$ subject and ending up with:
$$\frac{dy}{dx} = \frac{2(x^2+6xy-5y^2)}{7x(x-y)}$$
After simplifying the numerator: 
$$\frac{dy}{dx} = \frac{2[(x-y)(x+5y)+2xy]}{7x(x-y)}$$
$$\frac{dy}{dx} = \frac{2(x+5y)}{7x} + \frac{4y}{7(x-y)}$$
I have no idea how to proceed from here. Is the methodology correct so far? Any input would be appreciated.

Starting with your equation
$$\frac{dy}{dx} = \frac{2(x+5y)}{7x} + \frac{4y}{7(x-y)}$$
multiply the top and bottom of each fraction on the right, giving
$$\frac{dy}{dx} = \frac{2(x+5y)}{7x}\frac{1/x}{1/x} + \frac{4y}{7(x-y)}\frac{1/x}{1/x}$$
$$\frac{dy}{dx} = \frac{2(1+5y/x)}{7} + \frac{4y/x}{7(1-y/x)}$$
Since $y'=u'x+u$ you get
$$u'x+u = \frac{2(1+5u)}{7} + \frac{4u}{7(1-u)}$$
which is a separable differential equation.
