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  3. y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y�

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

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Advance Math

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2
y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t

y′ = 5t4y, y(0) = 1, solution: y(t) = et5
y′ = 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=0.1×2−k for0≤k≤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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