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Separable differential equation 
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#1
Feb413, 02:29 PM

P: 202

1. The problem statement, all variables and given/known data
I am asked to find a singular solution of the D.E. dy/dx = (xy+2yx2)/(xy3y+x3). I am first solving to find the general solution form of the D.E., and so far have it to: [(x+2)/(x3)]dx = [(y+1)/(y1)]dy From here, of course, you integrate both sides, but I am struggilng to find the best technique of integration. Any ideas? 2. Relevant equations 3. The attempt at a solution 


#2
Feb413, 02:48 PM

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P: 21,216

For example, (x + 2)/(x  3) = (x  3 + 5)/(x  3) = (x  3)/(x  3) + 5/(x  3) = 1 + 5/(x  3). The same sort of idea works with the other rational expression. 


#3
Feb413, 05:42 PM

P: 202

Thanks Mark. That helped. Can anyone also verify that y=1 is a singular solution to the D.E.?



#4
Feb413, 10:43 PM

P: 202

Separable differential equation
I have solution, which I disagree with, claiming y=0 is a singular solution since, upon substitution, it doesn't seem to produce an identity.



#5
Feb513, 12:22 AM

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P: 21,216

If y ##\equiv## 0 is a (purported) solution, then it follows that dy/dx ##\equiv## 0. However, if y = 0, from the diff. equation, we have dy/dx = (x  2)/(x  3), which is zero only if x = 2. 


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