Thread: Ordinary Differential Equation (quick question about a step in the process)

Looking through my notes for a maths exam tomorrow I can't figure out the jump from one step to another:

The original question is Solve:



now further down the steps I can't figure out how it jumps from:



to



What I want to know is how you get from the to the and what happens to the

Thanks

I think you have a typo in your problem, the original equation should be

As for your question, what do you get if you try to differentiate w.r.t. to the expression ?

I don't see any typo no, that's the notation we use for Ordinary Differential Equations.

Differentiating that will give you the yes, but what I think I'm meaning to say is, how do you jump from the to what is the difference between them.

And if you do as you say and differentiate w.r.t. to the expression ? How can this still be the same as the line up above it? Surely that would make it: and not

Or am I completely missing something here?

Originally Posted by Macca567

I don't see any typo no, that's the notation we use for Ordinary Differential Equations.

Differentiating that will give you the yes, but what I think I'm meaning to say is, how do you jump from the to what is the difference between them.

And if you do as you say and differentiate w.r.t. to the expression ? How can this still be the same as the line up above it? Surely that would make it: and not

Or am I completely missing something here?

You are missing something.



by the quotient rule and implicit differentiation.