My Math Forum Simplifying in diff eq

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 24th, 2015, 06:28 AM #1 Newbie   Joined: Jan 2015 From: Minnesota Posts: 2 Thanks: 0 Simplifying in diff eq So issue I am having involves the diff eq x * dy/dx = y + √(x² - y²) In my book it says to first divide both sides by x to get dy/dx = (y/x) + √(1 - (y/x)²) For the life of me, I do not understand how the first equation simplifies to the second one. Am I missing some fundamental fact about powers? Any help would be greatly appreciated. Last edited by skipjack; January 24th, 2015 at 07:48 AM.
 January 24th, 2015, 06:46 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond $\displaystyle \frac{\sqrt{x^2-y^2}}{|x|}=\frac{\sqrt{x^2-y^2}}{ \sqrt{x^2}}=\sqrt{\frac{x^2-y^2}{x^2}}=\sqrt{1- \left(\frac{y}{x}\right)^2}$ Thanks from McPhi
 January 24th, 2015, 07:44 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,809 Thanks: 2150 Does the book suggest one then makes a substitution? The substitution y = xu could have been done at the outset. It's best to consider x < 0 and x > 0 separately. What happens as x approaches zero is "interesting".
 January 24th, 2015, 08:21 AM #4 Newbie   Joined: Jan 2015 From: Minnesota Posts: 2 Thanks: 0 Sweet Ah. Thank you. I knew I just wasn't seeing it the right way. Yes that is the sub the book makes.

 Tags diff, simplifying

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Niko Bellic Calculus 2 July 8th, 2013 10:01 AM sasho_ Calculus 2 May 1st, 2012 06:26 AM FreaKariDunk Calculus 24 March 3rd, 2012 12:22 PM amaciose Calculus 5 October 12th, 2008 04:10 AM keeps14soccer Calculus 2 September 14th, 2008 04:56 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top