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 February 7th, 2017, 05:29 PM #1 Member   Joined: Feb 2014 Posts: 91 Thanks: 1 Find the general solution of the differential equation I'm having trouble finding the general solution of question 3. We just covered this and the teacher hasn't really covered everything but I want the headstart. I tried separating this but it doesn't seem to be working. Could anyone guide me? I wanna look like smart when I go back to class.  February 7th, 2017, 07:05 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,949 Thanks: 1555 Try typing it in next time ... it's just a single DE. $x \cdot \dfrac{dy}{dx}=y+2\sqrt{xy}$ $\dfrac{dy}{dx}=\dfrac{y}{x} + 2 \sqrt{\dfrac{y}{x}}$ Let $v = \dfrac{y}{x} \implies y=xv \implies \dfrac{dy}{dx}=x \cdot \dfrac{dv}{dx}+v$ $x \cdot \dfrac{dv}{dx} + v = v + 2\sqrt{v}$ $x \cdot \dfrac{dv}{dx} = 2\sqrt{v}$ $\dfrac{dv}{2\sqrt{v}} = \dfrac{dx}{x}$ $\sqrt{v}=\ln{x}+C$ $v= (\ln{x}+C)^2$ $y=x(\ln{x}+C)^2$ Thanks from greg1313, The_Ys_Guy and Joppy Tags differential, equation, find, general, solution 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 neelmodi Differential Equations 1 February 27th, 2015 06:34 AM dunn Differential Equations 2 February 19th, 2012 03:38 AM mbradar2 Differential Equations 7 October 12th, 2010 01:09 PM mbradar2 Differential Equations 7 September 25th, 2010 10:58 AM Ichigo Differential Equations 3 September 1st, 2008 10:06 AM

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