Find differential equation y ′ = f ( t , y ) satisfied by y...
Find differential equation satisfied by
Compute derivative of y,
Write right hand side above, in terms of the original function y, that is,
Get a differential equation satisfied by y, namely
So my issue with that last answer. How is this a solution? Does it mean that if you somehow take an integral of you should end up with the original ???
It seems that there two different derivatives of y(t)
the other is:
and I don't get it, can someone explain?
Also a bit offtopic, but the way y'=f(t,y) is written kinda bugs me.
Shouldn't it be written like y'=f(t,y(t)) to show that the function f contains t as an independent variable and the function y(t) which contains variable t as an input to itself (dependent variable t) ??? That's kinda an essential information, so surprised it's omitted in the writings.