24) Using Taylor method of order 2 to estimate the solution of the ODE y' = cos (xy?) ,y(1) = 2, h = 0.1 If y1= 1.94 . Find y2

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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24) Using Taylor method of order 2 to estimate the solution of the ODE
y' = cos (xy?) y(1) = 2, h = 0.1
If y1= 1.94
. Find y2
Transcribed Image Text:24) Using Taylor method of order 2 to estimate the solution of the ODE y' = cos (xy?) y(1) = 2, h = 0.1 If y1= 1.94 . Find y2
Expert Solution
Step 1

To estimate the solution of ODE we will use the following Taylor's series formula for second order:

y2=y1+hy1'+h22!y1''

we are given  y'=cos(xy2), y(1)=2, y(1.1)=y1=1.94, h=0.1, y(1.2)=y2=?

so we have x0=1, y0=2, y1=1.94, h=0.1, xn=1.2, n=xn-x0h=2

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