Learn how to solve problems step by step online. Solve the differential equation (y-(x^2+y^2)^(1/2))dx-xdy=0. We can identify that the differential equation \left(y-\sqrt{x^2+y^2}\right)dx-x\cdot dy=0 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 (y-(x^2+y^2)^(1/2))dx-xdy=0