Consider the differential equation dy dy 4=x? ху =1, where x <2 and y=1 when x= 0. (a) Use Euler's method withh=0.25 , to find an approximate value of y when x=1, giving your answer to two decimal places. The exact solution of this equation is y= v4-x² (sin" (0.5x)+0.5) (b) Show that your approximate value of y in (a) is greater than the true value of y. (c) Sketch the graph of y = f(x) for 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the differential equation
dy
dy 4=x?
ху
=1, where x <2 and y=1 when x= 0.
(a)
Use Euler's method withh=0.25 , to find an approximate value of y when x=1,
giving your answer to two decimal places.
The exact solution of this equation is y= v4-x² (sin" (0.5x)+0.5)
(b)
Show that your approximate value of y in (a) is greater than the true value of y.
(c)
Sketch the graph of y = f(x) for 0<x<1. Use your sketch to explain (b).
Transcribed Image Text:Consider the differential equation dy dy 4=x? ху =1, where x <2 and y=1 when x= 0. (a) Use Euler's method withh=0.25 , to find an approximate value of y when x=1, giving your answer to two decimal places. The exact solution of this equation is y= v4-x² (sin" (0.5x)+0.5) (b) Show that your approximate value of y in (a) is greater than the true value of y. (c) Sketch the graph of y = f(x) for 0<x<1. Use your sketch to explain (b).
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