This equation is supposedly separable:
but I can't separate it with algebra, and the substitutions I've tried (v=y/t, v=(t^2 + y^2)^1/2) haven't worked. The full problem, if it makes a difference, is to solve for the initial value y(1) = 0.
Could you give me a hint please?
That makes sense, thank you. After substituting and rearranging I get this:
And after integrating:
and plugging in the initial value gives me
so c = 0.
However the answer in the back of the book is . Could you please tell me where I'm messing up?
Also, out of curiosity, is there any time when it'd be useful to make a substitution other than y/t in a problem like this? For example, t/y?
I thought I hit discrete mathematics topic but I guess not. Just happened to look at this and the question that came to mind for me, and forgive my ignorance if not because I have yet to have this subject, would the sq root in the denominator have an impact in following processes?