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Calculus - Numerical Analysis - Approximations

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Use Modified Euler's Method to approximate the solution to the initial value problem
and compare the results to the actual values
y'=1+(t-y)^2 , 2 <=t<=3 , y(2) = 1 with h = 0.5

Actual solution y(t)=t+1/(1-t)

For full description of the question, please see the attached question file

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Solution Summary

The posted problem is solved using step by step method and explanation and all the working.
It facilitates students to use this solution to solve other similar problems.

Using Modified Euler's Method y(2.5) = 1.868164 and y(3) = 2.526854

Values from actual solution are y(2.5) = 1.833333 and y(3) = 2.5

For detailed step by step solution of the problem with all working, please see the attached solution file.
For detailed step by step solution, please see the attached solution file.

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Using Modified Euler's Method y(2.5) = 1.868164 and ...

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