dx+ydy=x^2 ydy


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 127743 by arash sharifi last updated on 01/Jan/21

$d x + y d y = x^{2} y d y$
Commented by mr W last updated on 01/Jan/21

$y o u h a v e a s k e d t h e s a m e q u e s t i o n$ $b e f o r e a n d i t w a s a n s w e r e d!$
	Answered by Olaf last updated on 01/Jan/21

	$d x + y d x = x^{2} y d y$ $d x = y (x^{2} - 1) d y$ $\frac{d x}{x^{2} - 1} = y d y$ $\frac{1}{2} [\frac{1}{x - 1} - \frac{1}{x + 1}] d x = y d y$ $\frac{1}{2} \ln ∣ \frac{x - 1}{x + 1} ∣ = \frac{1}{2} y^{2} + C_{1}$ $y = \pm \sqrt{\ln ∣ \frac{x - 1}{x + 1} ∣ + C_{2}}$
	Answered by ZaidMNuri last updated on 01/Jan/21

	$d x = (x^{2} - 1) y d y$ $\frac{d x}{(x^{2} - 1)} = y d y$ $\int \frac{d x}{(x^{2} - 1)} = \int y d y$ $\frac{1}{2} \int [\frac{1}{x - 1} - \frac{1}{x + 1}] d x = \frac{y^{2}}{2} + C$ $\frac{1}{2} l n ∣ \frac{x - 1}{x + 1} ∣= \frac{y^{2}}{2} + C$ $y = \mp \sqrt{l n ∣ \frac{x - 1}{x + 1} ∣ - 2 C}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum