# Differential equation using Improved Euler’s method

#### Kipkorir

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Problem 2: Consider the following Initial Value Problem (IVP) where (𝑡) is the dependent function:
𝑦 ′ = 𝑦 − 𝑦 2 + 1.14 cos(𝑒 𝑡/2 ) with 𝑦(0) = 𝑦0 and 𝑡 ≥ 0
Part 2A:
Approximate the solution to the IVP using the Improved Euler’s method with the following conditions: Initial condition 𝑦0 = 1; time steps ℎ = 1 8 , 1 16 , 1 32 , 1 64 ; and time interval 𝑡 ∈ [0,20]
Plot the Improved Euler’s method approximation for all 4 time steps
Discuss the results of these approximations