y t, y(0) 1, solution y(t) 1 t2 2 y 2(t 1)y, y(0) 1, solu...

yâ€² = t, y(0) = 1, solution: y(t) = 1+t2/2 yâ€² = 2(t + 1)y, y(0)...

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yâ€² = t, y(0) = 1, solution: y(t) = 1+t2/2
yâ€² = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t
yâ€² = 5t4y, y(0) = 1, solution: y(t) = et5
yâ€² = t3/y2, y(0) = 1, solution: y(t) = (3t4/4 + 1)1/3
For the IVPs above, make a log-log plot of the error of BackwardEuler and Implicit Trapezoidal Method, at t = 1 as a function ofhwithh=0.1Ã—2âˆ’k for0â‰¤kâ‰¤5.

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MATLAB CodeBackward Eulerclose allclearclck 015H 01 2kyexact t 1 t2 2y1 1 Initial conditionti 0 tf 1 Interval of tyfvec Vector for storing yt 1 for different stepsizesfor i 1lengthHh Hit tihtffor j 1lengtht1syms ynextsol solveynext yj htj1 Solve foy ynextsol sol1yj1 doublesol Backward Euler Updateendyfvec yfvec yend Store the value of yt 1endfigure loglogH absyexact1 yfvec o xlabelhylabelErrortitlesprintfLogLog plot of Error of Backward Eulers Method att 1nODE y tyexact t expt2 2ty1 1 Initial conditionti 0 tf 1 Interval of tyfvec Vector for storing yt 1 for different stepsizesfor i 1lengthHh Hit tihtffor j 1lengtht1syms ynextsol solveynext yj h2tj1 1ynext Solvefoy ynextsol sol1yj1 doublesol See Answer

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