Solve the sepereable D.E.
xdy = y*ln(y)dx , x = 2 , y = e
I started by dividing both sides by y*ln(y) and x to wind up with
dx/x = dy/(y*ln(y))
Then I go to integrate and end up with
ln(x) + C = ln(ln(y)) + C
And then I'm stuck. I'm entirely unsure of where to go with this. Any ideas? Thank you
- Charles
Ok. So I can ln the constant because it doesn't change anything, it's still a constant, right? So from
ln|x| = ln|lny| + ln|k|
I e everything right? e^ln|x| = e^ln|lny| + e^ln|k|
which leaves
x = lny + k
lny = x - k
y = e^x - e^k => e^x - k
k = e^x - y , x = 2, y = e
k = e^2 - e^1 = 4.6708
Is that correct?
Am I allowed to e everything like that?