I have a question on the particular case of the Cauchy theorem for a first order differential equation with separable variables.
If I impose:
continuous in a interval
continuous and with continuous derivative in a interval
Can I say that there is only one solution in all the interval I that satisfies the condition of passage through a point ?
Or, instead of the continuity of the derivative of , should I impose that the derivative of is limited on ?
Can anyone suggest me the correct conditions to impose in this particular case?
Thanks in adivce