I am told I can use the substitution
I have to following differential equation. I need to solve it. I have gotten so far but got stuck... I have tried solving the equation using seperation of variables, which I think is where I've gone wrong. This is the equation:
Is seperation of variables the way to go, i.e, should I start by dividing through by:
thanks Dan for the explanation. Your method it the method I am supposed to be using, although, no doubt CB and Mr Fantastic's methods are equally correct.
However, could you explain what you have done there because I don't truly understand how you've achieved it...
I'm sorry, that was a bit vague, how does what you have done fit in with the integration by substitution rule, i.e,
where
Hope you don;t mind me using S's as integral signs, don't know how to do them in latex and double clicking yours brings up an error ?
You don't necessarily need to do it, it just makes the form of the integrand simpler. (When the concept works, that is.) In this case integrating is harder to integrate than . This case is almost trivial because it is not hard to see how to integrate the expression in v, but your integrand might be more complicated, such as for which the substitution of makes the problem much simpler.
-Dan