Use Euler's method to approximate y(1.8). Start with step size h = 0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimal places. y=x² + y²-2. y(0) = 0 The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between (Type an integer r decimal rounded to two decimal places as needed.) ▾So, a good approximation of y(1.8) is.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use Euler's method to approximate y(1.8). Start with step size h=0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimal
places.
y'=x² + y²-2. y(0) = 0
The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between
(Type an integer or decimal rounded to two decimal places as needed.)
▾ So, a good approximation of y(1.8) is.
Transcribed Image Text:Use Euler's method to approximate y(1.8). Start with step size h=0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimal places. y'=x² + y²-2. y(0) = 0 The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between (Type an integer or decimal rounded to two decimal places as needed.) ▾ So, a good approximation of y(1.8) is.
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