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 November 27th, 2017, 07:52 AM #1 Newbie   Joined: Apr 2014 From: Canada Posts: 4 Thanks: 0 Singular solution How to show that $\displaystyle t=0$ is a solution of $\displaystyle 2t^2e^{-x}\,dt+x\sqrt{t}\,dx=0$? I do not know how to calculate $\displaystyle dt$ when $\displaystyle t=0$. Thanks. Last edited by eulid; November 27th, 2017 at 08:18 AM.
 November 27th, 2017, 09:51 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 The way you have phrased this is a little confusing. A first order equation like this can be thought of as an equation describing x as a function of t or as an equation describing t as a function of x. The best I can do in interpreting your question is that you want to show that t, as a function of x, is the constant function t= 0 no matter what x is. In that case, since t is a constant, the derivative is 0: dt/dx= 0 so dt= 0 while dx can be anything. Set t= 0 and dt= 0 and show that the equation is satisfied for all x. Thanks from eulid
 November 27th, 2017, 11:17 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra You don't even need $\mathrm dt$ or $\frac {\mathrm dt}{\mathrm dx}$ for this. $t=0$ is sufficient. Thanks from eulid

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