(2xy) dx + (x^2 + 2y) dy = 0; x^2 y + y^2 = c

(2xy) dx + (x^2 + 2y) dy = 0; x^2 y + y^2 = c find the solution
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1 Answer

x²y+y²=c implicitly differentiated wrt x: (2xy+x²dy/dx)+2ydy/dx=0.

This is the same as 2xydx+x²dy+2ydy=0=2xydx+dy(x²+2y)=0.

Therefore the solution is x²y+y²=c, where c is a constant.
by Top Rated User (1.2m points)

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