Heard of it, never knew what it was.Originally Posted by ThePerfectHacker
-Dan
OK, the section of the book in which the question lies has the other questions done by substitution but I couldn't do this one.Originally Posted by ThePerfectHacker
Taking where & are variables
So,
and
On differentiating the above two equations we can substitute & in the differential equation.
So does this help?
First, is this equation correct? Usually if there's an "e" in there it's or something.Originally Posted by shubhadeep
Let's try:
or the form
This kind of non-linear first order differential equation is a "Bernoulli" equation with n = -1.
Let . Then , or .
Thus:
Thus
which is now a linear first order differential equation, which you can solve using any method you wish. (Remember to back-substitute to get y(x)!)
-Dan
I've tried the polar coordinate substitution you suggested, but I'm not getting any "joy" out of it.