2 2 satisfying the initial conditions 0 1 on interval

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?? = 2? 2 satisfying the initial conditions ?(0) = 1 on interval [0, 1] with ℎ = 0.2 . Euler’s Method: ?? ?? = 2? 2 = ?(?, ?) ? 𝑖+1 = ? 𝑖 + ?(? 𝑖 , ? 𝑖 )ℎ ⇒ ? 𝑖+1 = ? 𝑖 + 2? 𝑖 2 ? 0 = 0, ? 0 = 1 See the table below for results. (d) Find the differences between actual solution and Euler’s approximation at ? = 0.2 , ? = 0.4 , ? = 0.6 , ? = 0.8 and ? = 1 . 𝑖 ? 𝑖 Actual Solution ?(? 𝑖 ) Euler's Method ? 𝑖 Difference ? 𝑖 − ?(? 𝑖 ) 0 0 1 1 0 1 0.2 1.005333 1 -0.00533 2 0.4 1.042667 1.016 -0.02667 3 0.6 1.144 1.08 -0.064 4 0.8 1.341333 1.224 -0.11733 5 1 1.666667 1.48 -0.18667
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