3. Given the initial value problem y' = (2/t)y + t'e', 1

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3 Given The Initial Value Problem Y 2 T Y T E 1 T 2 Y 1 0 With Exact Solution Y T Te E A Use Euler 1 (41.82 KiB) Viewed 31 times

3. Given the initial value problem y' = (2/t)y + t'e', 1<t< 2 y(1) = 0) with exact solution y(t) = te - e) (a) Use Euler's method with h 0.1 to approximate the solution and compare it with actual values of y. (b) Use the answers generated in part (a) and linear interpolation to approximate the following values of y and compare them to the actual values. i. y(1.04), ii. y(1.55), iii. y(1.97). (c) Compute the value of h necessary for \y(t;) – uz < 0.1 using the formula below hM ly-us (el(t.-a) - 1) 2L where a <t<b, \y"O SMVt € [a, b] and L is the Lipschitz constant for f(y,t).