MAT244--2020F > Chapter 2

Textbook Section2.1 Example5


Hi guys, I have been stuck at example 5 of section2.1(page30) for quite a while. In particular, I do not understand why the lower bound of the integral is the initial point t=0. Why can't it be the upper bound?
(example screenshot is attached below)

In my opinion, firstly this question is an initial value problem, which means the number that the equation (y(0)=1) gives you is the lower limit of the integral, which is 0. You can also use the upper bound, however, if t is infinity, then we can not substitute t as a number into the equation and then solve it. In this way, choosing the lower limit number 0 is the easiest and the fastest method.

Victor Ivrii:
You can select any lower limit you wish, the difference goes to the constant. However, as Ella correctly observed, it makes sense to select $t=0$ since the $t_0=0$ in the initial problem


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