Learn how to solve problems step by step online. Solve the differential equation (x^2+2y^2)dx=xydy. We can identify that the differential equation \left(x^2+2y^2\right)dx=xy\cdot dy is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, 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.

Solve the differential equation (x^2+2y^2)dx=xydy