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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 June 17th, 2017, 12:32 PM #1 Member   Joined: Jun 2017 From: India Posts: 65 Thanks: 3 A beginner differential equation question What is a differential equation ? It is an equation involving an unknown function (solution) and its derivatives .   June 17th, 2017, 12:51 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2215 The function (of x) is y, and dy/dx is its derivative (with respect to x). Thanks from awholenumber June 17th, 2017, 04:33 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 If you are asking whether $\displaystyle y= \pm\sqrt{\frac{2}{3}x^3+ C}$ really does satisfy $\displaystyle \frac{dy}{dx}= \frac{x^2}{y}$, it is easy to check. First, squaring both sides gives $\displaystyle y^2= \frac{2}{3}x^3+ C$ and differentiating both sides with respect to x, $\displaystyle 2y\frac{dy}{dx}= 2x^2$. Dividing both sides by 2y, $\displaystyle \frac{dy}{dx}= \frac{x^2}{y}$, precisely the differential equation you started with. Or, more directly but more complicated, differentiating the original formula with respect to x, $\displaystyle \frac{dy}{dx}= \pm\frac{1}{2}\left(\frac{2}{3}x^3+ C\right)^{-1/2}(2x^2)= \frac{x^2}{\pm\sqrt{\frac{2}{3}x^3+ C}}= \frac{x^2}{y}$. Thanks from awholenumber Last edited by skipjack; June 17th, 2017 at 05:16 PM. June 17th, 2017, 10:17 PM #4 Member   Joined: Jun 2017 From: India Posts: 65 Thanks: 3 Thanks , Found some good materials here National Council Of Educational Research And Training :: Home  Tags beginner, differential, equation, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post colinzeal Algebra 5 September 30th, 2013 03:35 PM hogan Differential Equations 4 June 4th, 2012 11:02 AM phss Calculus 2 January 19th, 2011 10:08 AM and1bball4mk Differential Equations 2 January 13th, 2010 07:10 AM Kevlarji Differential Equations 1 September 26th, 2009 03:25 PM

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