Full answer: The method outlined in can be used for any homogeneous equation. That is
Chapter 2, Problem 31(choose chapter or problem)
The method outlined in can be used for any homogeneous equation. That is, the substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by y/x gives the solution to the original equation. In each of 31 through 38: (a) Show that the given equation is homogeneous. (b) Solve the differential equation. (c) Draw a direction field and some integral curves. Are they symmetric with respect to the origin?dydx = x2 + xy + y2x2
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