Help with solutions to two DEs
- From: carlos5100@xxxxxxxxx
- Date: 24 Jun 2005 12:05:00 -0700
Hello,
I think I have solved these two DEs below correctly, but I am not
really sure about my concussion on there interval of existence and was
wondering if someone could tell me if I am right or wrong. If I am
wrong, I would greatly appetite an explanation why.
First DE
(x^2+1)dy/dx=xy^2+x
Moving things around gives us
dy/((y^2+1)dx)-x/(x^2+1)=0
Integrating gives us, after moving things around again.
InverseTan(y)=c+ln(x^2+1)/2
Thus,
y=tan(c+ln(x^2+1)/2)
Now since InverseTan is defined by, y=InverseTan(x) if and only if
tan(y)=x and -Pi/2<y<Pi/2, we have that the solution is valid for the
interval Sqrt[e^(-Pi-C)-1]<x< Sqrt[e^(Pi-C)-1], correct?
Second DE
e^x(y^2-4y)dx+4dy=0
Moving things around gives us
dy/((y^2-4y)dx)+e^x/4=0
integrating, we find.
ln(|y-4|/|y|)/4+e^x/4=C
moving things around
ln(|y-4|/|y|)=-e^x+C
and since we cannot not solve for y we cannot determine the interval
the solution is valid for, correct?
Thanks a lot for your help guys.
Sam J.
.
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