- Use Euler's method to obtain a numer- ical solution of the differential equation dy = 3 -2, with the initial conditions that dr x=1 when y=2, for the range x=1.0 to x=1.5 with intervals of 0.1. Draw the graph of the solution in this range. 1.0 1.1 2 2.1 1.2 2.209091 1.3 2.325000 2.446154 2.571429 1.4 1.5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Use Euler's method to obtain a numer-
ical solution of the differential equation
dy
= 3
dr
with the initial conditions that
x=1 when y=2, for the range x=1.0 to
x=1.5 with intervals of 0.1. Draw the graph
of the solution in this range.
y
1.0
1.1
2
2.1
1.2
2.209091
1.3
2.325000
1.4
2.446154
1.5
2.571429
dy
+1= -!
dr
(a) The differential equation
has the initial conditions that y=1 at
x=2. Produce a numerical solution of
the differential equation in the range
x=2.0(0.1)2.5.
(b) If the solution of the differential equa-
tion by an analytical method is given by
4 x
y= -- determine the percentage error
at x=2.2.
Transcribed Image Text:1. Use Euler's method to obtain a numer- ical solution of the differential equation dy = 3 dr with the initial conditions that x=1 when y=2, for the range x=1.0 to x=1.5 with intervals of 0.1. Draw the graph of the solution in this range. y 1.0 1.1 2 2.1 1.2 2.209091 1.3 2.325000 1.4 2.446154 1.5 2.571429 dy +1= -! dr (a) The differential equation has the initial conditions that y=1 at x=2. Produce a numerical solution of the differential equation in the range x=2.0(0.1)2.5. (b) If the solution of the differential equa- tion by an analytical method is given by 4 x y= -- determine the percentage error at x=2.2.
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