Toronto Math Forum
MAT2442020F => MAT244Lectures & Home Assignments => Chapter 2 => Topic started by: yingxuanwang on September 19, 2020, 09:11:39 PM

Hi, I have a question when I solve the general solution of ODE.
When I calculate the integral, should I add the absolute value to the result? (see the picture)
I am confused about this because I think the constant "C" can cancel the absolute value there.
Also, can anyone help me to check if my answer totally correct or anywhere I can improve?
Look forward to a kind reply.
Thanks a lot! :)

For your first question, the integral should be the absolute value.
However, when you are doing such problems, I believe that you can just assume everything in the absolute value symbol is positive because you already had a constant C (except for some cases that have a restriction on the variables). Also, I think your answer is correct and wellwritten.
Correct me if I'm wrong! ;)

I am still a little bit confused. So for this question, the result of the integral does not need to contain absolute value right? Or I need to write it in two lines: 1st line is with the absolute value and constant C1, 2nd line is without the absolute value and constant C?

Read W2L1 handout. THere is an explanation

The integral should have the absolute value, but for this question, your result don't need it. In your process, you can remove the absolute value because constant C can be positive, negative or 0. You can read the 8th page of the slide to see details.