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

Consider the following Initial Value Problem (IVP) where y(t) is the dependent function: y' = y - yz + 1.14 cos(et/2) with y(0) = yo and t 2 0 Part A: Approximate the solution to the IVP using the Improved Euler's method with the following conditions: Initial condition yo = 1; time steps h = , , ,; and time interval t c [0,20] + Plot the Improved Euler's method approximation for all 4 time steps + Discuss the results of these approximations Part B: Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition yo = 1; time steps h = _,,,-; and time interval t 6 [0,20] + Plot the RK4 approximation for all 4 time steps + Discuss the results of these approximations

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