Solve the differential equation (1+y^2 )dx−(1+x^2 )xydy=0


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Question Number 175670 by Engr_Jidda last updated on 04/Sep/22

$S o l v e t h e d i f f e r e n t i a l e q u a t i o n$ $(1 + y^{2}) d x - (1 + x^{2}) x y d y = 0$
	Answered by mahdipoor last updated on 04/Sep/22

	$\Rightarrow (1 + y^{2}) d x = (x + x^{3}) y d y$ $\Rightarrow \frac{d x}{x + x^{3}} = \frac{y d y}{1 + y^{2}} \Rightarrow$ $\int (\frac{1}{x} - \frac{x}{x^{2} + 1}) d x = \frac{1}{2} \int \frac{2 y d y}{(1 + y^{2})} \Rightarrow$ $l n ∣ x ∣ - \frac{1}{2} l n (x^{2} + 1) = \frac{1}{2} l n (y^{2} + 1) + l n C \Rightarrow$ $\frac{x}{\sqrt{1 + x^{2}}} = C \sqrt{1 + y^{2}}$
	Commented by Engr_Jidda last updated on 05/Sep/22

	$t n a n k y o u b o s s$
	Commented by peter frank last updated on 05/Sep/22

	$thanks$
	Commented by mahdipoor last updated on 05/Sep/22

	$♡$
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