Final answer to the problem
$y=C_1x^2$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^2+2xydx-x^2dy=0. We can identify that the differential equation y^2+2xy\cdot dx-x^2dy=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: 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.
Final answer to the problem
$y=C_1x^2$
