# differential equation question

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• October 31st 2008, 02:25 AM
ADARSH
differential equation question
(Hi)Hello everyone

$
\frac{x}{y} = t ,$

$
\int [(1+e^t) dx + (1-t)e^t dy] = 0
$

find soln.(Nerd)?
• October 31st 2008, 03:22 AM
Peritus
• October 31st 2008, 05:10 AM
HallsofIvy
Quote:

Originally Posted by ADARSH
(Hi)Hello everyone

$
\frac{x}{y} = t ,$

$
\int [(1+e^t) dx + (1-t)e^t dy] = 0
$

find soln.(Nerd)?

At first I thought the "t" was a distraction and wrote out the whole problem in terms of x and y only. It was easy to see that the result was an "exact differential" just as Peritus said. However, then I could not see any way to integrate that exact differential!

But if t= x/y, the x= yt and dx= ydt+ tdy. In terms of t and y only the differential becomes [tex](1+ e^t)(ydt+ tdy)+ (1-t)e^t dy= (t+ e^t)dt+ y(1+ e^t)dy and that's easy to integrate!