Solve the ODE:
3. The attempt at a solution
My teacher hinted that the substitution could be helpful, but once I make the substitution, I can't seem to take the next step.
Differentiating WRT x, we have:
Substituting back in we have:
But I can't take it from here... much less obtain an equation for y(x). Any thoughts?
That looks OK: http://www.wolframalpha.com/input/?i...-+y%5E2%5D%2Fy
(Note that the form given by Wolfram is not the simplest)
I just want to point out that there are integrals of the following type
that can be solved only in three cases:
- substitute where is the denominator of the fraction
- substitute where again is the denominator of the fraction
The integral here is one such integral in which , and . Notice that hence it can be solved using the substitution
Of course, your teacher gave you that as a hint, and you and the rest of the crew here solved the problem. I think it is worth noting that this integral is nothing special.