Plot the solution using matlab a) Method of Undetermined Coefficients: The differential equation d-d-et at

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Plot the solution using matlab
a.) Method of Undetermined Coefficients:
The differential equation
d-d-et
Then if yet be a trial solution then
auxiliary equation is
m²-m=0
So complementary function is
Aet +Be B+ het
The right hand side contain et of which
1 is a simple root of the auxiliary
equation. So we take ctet)as
particular solution.
m-1,0.
Then
d (etet) - de (e ett) = et
c{tet +2et-c{tet+ et} = et
dt²
>>cet=et
C-1
so particular solution is
So general solution is
y = Re² + B + te¹.
and
Now y(o)=0
O = A + B
and
Both gives A=-1
= tet
y=
y'(o)=0 gives
o = A + 1
and B-1
Hence required solution is
y=1-e² + te
Transcribed Image Text:Plot the solution using matlab a.) Method of Undetermined Coefficients: The differential equation d-d-et Then if yet be a trial solution then auxiliary equation is m²-m=0 So complementary function is Aet +Be B+ het The right hand side contain et of which 1 is a simple root of the auxiliary equation. So we take ctet)as particular solution. m-1,0. Then d (etet) - de (e ett) = et c{tet +2et-c{tet+ et} = et dt² >>cet=et C-1 so particular solution is So general solution is y = Re² + B + te¹. and Now y(o)=0 O = A + B and Both gives A=-1 = tet y= y'(o)=0 gives o = A + 1 and B-1 Hence required solution is y=1-e² + te
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