### Author Topic: Lec 0101 - 9/15 Question  (Read 407 times)

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##### Lec 0101 - 9/15 Question
« 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?
« Last Edit: September 20, 2020, 06:18:46 PM by Brandon Adiwinata »

#### RunboZhang

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##### Re: Lec 0101 - 9/15 Question
« Reply #1 on: September 20, 2020, 07:12:43 PM »
Hi, I have plugged it in y and calculated the LHS. Computation is attached below.

#### Victor Ivrii

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##### Re: Lec 0101 - 9/15 Question
« Reply #2 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