Question: Problem 2: Consider the following Initial Value Problem (IVP) where y(t) is the dependent function: y' = y-y + 1.14 cos(et/2) with y(0) =

Problem 2: Consider the following Initial Value Problem (IVP) where y(t) is the dependent function: y' = y-y + 1.14 cos(et/2) with y(0) = yo and t 0 Part 2A: Approximate the solution to the IVP using the Improved Euler's method with the following 1 1 1 conditions: Initial condition yo = 1; time steps h = = and time interval t [0,20] 8'16'32'64' Project 1 + Plot the Improved Euler's method approximation for all 4 time steps + Discuss the results of these approximations Part 2B: Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition yo = 1; time steps h = 1,11 1 ; and time interval t [0,20] 8' 16'32'64' + Plot the RK4 approximation for all 4 time steps + Discuss the results of these approximations

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