I have the following example from a differential equations course, what I dont understand is how are you allowed to substitute A into the equation without any reason and why is it not put back in the end? This way seems easier but I dont understand the motivation behind A
I have the following example from a differential equations course, what I dont understand is how are you allowed to substitute A into the equation without any reason and why is it not put back in the end? This way seems easier but I dont understand the motivation behind A
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 28RE
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I have the following example from a differential equations course, what I dont understand is how are you allowed to substitute A into the equation without any reason and why is it not put back in the end? This way seems easier but I dont understand the motivation behind A
Transcribed Image Text:Eq) solve de la
ау
da
Aros.
=
у-аху
dy = y(1-4x)
Say = √(-4x) dx ✓
duly) = x-2x² +c
y(c) = e
²
y = € ex-2x ²6
x-2x²
= A é
using IC, y(a) = e
G
e= Aeº = A
=e
y=e'ex-2
x-2x²+1
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When is it allowed to use arbitrary constants in differential equations? So you dont need to substitute it back to its orginal form?
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