Toronto Math Forum
MAT2442020F => MAT244Lectures & Home Assignments => Chapter 2 => Topic started 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?

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

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