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Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and...

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Advance Math

Problem 1: Consider the following Initial Value Problem (IVP)where ? is the dependent variable and ? is the independentvariable: ??=sin(?)?(1??) with ?(0)=?0 and ? ? 0

Note: the analytic solution for this IVP is: y(t) =1+(y_0 - 0)e^cos(t)-1

Part 1B: Approximate the solution to the IVP using the ImprovedEuler’s method with the following conditions: Initial condition?0=?1/2; time step ?=1/16; and time interval ??[0,20]
+ Derive the recursive formula for the Improved Euler’s methodapplied to this IVP
+ Plot the Improved Euler’s method approximation
+ Plot the absolute error between the approximation and the exactsolution using a semilog plot

I'm having problems correctly codding these steps. Please typeout.

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