Final answer to the problem
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(x^2+3y^2)/(2xy). We can identify that the differential equation \frac{dy}{dx}=\frac{x^2+3y^2}{2xy} 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: y=ux. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.