(2x(√x)+x^2 +y^2 )dx+2y(√x)dy=0


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Question Number 26198 by sorour87 last updated on 22/Dec/17

$(2 x \sqrt{x} + x^{2} + y^{2}) d x + 2 y \sqrt{x} d y = 0$
	Answered by ajfour last updated on 22/Dec/17

	$l e t x^{2} + y^{2} = r^{2}$ $\Rightarrow x d x + y d y = r d r$ $s o (2 x \sqrt{x} + x^{2} + y^{2}) d x + 2 y \sqrt{x} d y = 0$ $b e c o m e s$ $2 \sqrt{x} (x d x + y d y) + (x^{2} + y^{2}) d x = 0$ $o r 2 \sqrt{x} (r d r) + r^{2} d x = 0$ $\Rightarrow \frac{d r}{r} + \frac{d x}{2 \sqrt{x}} = 0$ $\Rightarrow \ln r + \sqrt{x} = c$ $o r \frac{1}{2} \ln (x^{2} + y^{2}) + \sqrt{x} = c .$
	Commented by sorour87 last updated on 22/Dec/17

	$t h a n k y o u$
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