MAT244--2020F > Chapter 2

Lec5101 Question Mock Quiz 1

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yingxuanwang:
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! :)

Lingfei Li:
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 well-written.
Correct me if I'm wrong!  ;)

yingxuanwang:
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?

Victor Ivrii:
Read W2L1 handout. THere is an explanation

Lingfei Li:
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.