I'm watching some MIT OCW and the professor says in relation with the function y=e^x :

We start the function at y=1What I don't understand is...Why do we add that x? I understand why we start the differential equation at 1 but I do not understand why he insists that this x has to be added.

This has to be equal to its derivative so dy/dx=1

But I can't stop here...I must add an x to the function so that its slope will be one...So y=1+x...But now they need to be equal so I must add that x to dy/dx so dy/dx=1+x...

Thank you.