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Math Help - differential equation question

  1. #1
    Like a stone-audioslave ADARSH's Avatar
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    Question differential equation question

    Hello everyone

     <br />
\frac{x}{y} = t ,

    <br />
\int [(1+e^t) dx + (1-t)e^t  dy]  =  0 <br />

    find soln.?
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  2. #2
    Senior Member Peritus's Avatar
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  3. #3
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    Quote Originally Posted by ADARSH View Post
    Hello everyone

     <br />
\frac{x}{y} = t ,

    <br />
\int [(1+e^t) dx + (1-t)e^t  dy]  =  0 <br />

    find soln.?
    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!
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