the integral limit at ode with integration factor

almi23

New member
Joined
Oct 28, 2019
Messages
1
hey everyone, please help me.
how to they get to the integral limits?
why t goes from 1 and not from any other number?
 

Attachments

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,373
The lower limit is chosen arbitrarily. Changing it to , say, \(\displaystyle x_0\), would just add a constant (the integral from 1 to \(\displaystyle x_0\)) times \(\displaystyle e^t\) which would then become part of the first "\(\displaystyle c_1e^t\)". The upper limit is, of course, the variable, t.
 
Top