Subjects
Applied Mathematics for Electrical Engineering - 3130908
Complex Variables and Partial Differential Equations - 3130005
Engineering Graphics and Design - 3110013
Basic Electronics - 3110016
Mathematics-II - 3110015
Basic Civil Engineering - 3110004
Physics Group - II - 3110018
Basic Electrical Engineering - 3110005
Basic Mechanical Engineering - 3110006
Programming for Problem Solving - 3110003
Physics Group - I - 3110011
Mathematics-I - 3110014
English - 3110002
Environmental Science - 3110007
Software Engineering - 2160701
Data Structure - 2130702
Database Management Systems - 2130703
Operating System - 2140702
Advanced Java - 2160707
Compiler Design - 2170701
Data Mining And Business Intelligence - 2170715
Information And Network Security - 2170709
Mobile Computing And Wireless Communication - 2170710
Theory Of Computation - 2160704
Semester
Semester - 1
Semester - 2
Semester - 3
Semester - 4
Semester - 5
Semester - 6
Semester - 7
Semester - 8
Applied Mathematics for Electrical Engineering
(3130908)
AMEE-3130908
Winter-2019
Question-4c ( i )-OR
BE | Semester-
3
Winter-2019
|
26-11-2019
Q4) (c ( i ))
3 Marks
Attempt the following.
Solve the Ricatti’s equation
y
'
=
x
2
+
y
2
using the Taylor’s series method for the initial condition
y
(
0
)
=
0
. Where,
0
≤
x
≤
0
.
2
.
The Ricatti’s equation is,
y
'
=
x
2
+
y
2
Therefore,
f
x
,
y
=
x
2
+
y
2
Now,
y
(
0
)
=
0
⇒
y
0
=
0
,
x
0
=
0
By Taylor’s method,
y
x
n
=
y
n
=
y
n
-
1
+
h
1
!
y
n
-
1
'
+
h
2
2
!
y
n
-
1
'
'
+
⋯
Where,
x
n
=
x
0
+
nh
;
n
=
1
,
2
,
3
,
.
.
.
Now,
y
1
=
y
0
+
h
1
!
y
0
'
+
h
2
2
!
y
0
'
'
+
h
3
3
!
y
0
'
'
'
+
⋯
y
'
=
f
(
x
,
y
)
=
x
2
+
y
2
⇒
y
0
'
=
0
+
0
=
0
y
'
'
=
2
x
+
2
y
y
'
⇒
y
0
'
'
=
2
0
+
2
0
0
=
0
y
'
'
'
=
2
+
2
y
y
'
'
+
2
y
'
2
⇒
y
0
'
'
'
=
2
+
2
0
0
+
2
0
2
=
2
Then by Taylor’s series,
y
x
1
=
y
1
=
y
0
+
h
1
!
y
0
'
+
h
2
2
!
y
0
'
'
+
h
3
3
!
y
0
'
'
'
+
⋯
y
(
x
1
)
=
y
1
=
1
+
0
.
2
1
!
0
+
0
.
2
2
2
!
0
+
0
.
2
3
3
!
2
+
⋯
y
(
x
1
)
=
0
.
0027
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