Toronto Math Forum

MAT244--2020F => MAT244--Lectures & Home Assignments => Chapter 2 => Topic started by: Brandon Adiwinata on September 20, 2020, 06:16:36 PM

Title: Lec 0101 - 9/15 Question
Post by: Brandon Adiwinata on September 20, 2020, 06:16:36 PM

I had a question from the lecture about the Methods for solving a differential equation. As indicated in the photo, how do we get u'(sqrt(t^2+1)) = t after plugging in y = u(sqrt(t^2+1)) into the original inhomogeneous equation?

Title: Re: Lec 0101 - 9/15 Question
Post by: RunboZhang on September 20, 2020, 07:12:43 PM

Hi, I have plugged it in y and calculated the LHS. Computation is attached below.

Title: Re: Lec 0101 - 9/15 Question
Post by: Victor Ivrii on September 20, 2020, 07:49:47 PM

One should remember that plugging $y=uy_1$ into inhimogeneous equation leaves $u'y_1$ in the left-hand expression. If you do not remember this, therefore you just do not understand the method of variations and you should reread previous slides