Learn how to solve problems step by step online. Solve the differential equation dy/dx=(4y^2+xy)/(2xy-y^2). We can identify that the differential equation \frac{dy}{dx}=\frac{4y^2+xy}{2xy-y^2} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: x=uy. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to y.

Solve the differential equation dy/dx=(4y^2+xy)/(2xy-y^2)