Question

Help Entering Answers See Example 1.6.5, in Section 1.6, in the MTH 235 Lecture Notes. (1 point) , of approximate (a) Use the Picard-Lindeloef iteration to find a sequence {yn solutions to the initial value problem y'(t) = 8t+ y(t), y(0) = 5. yo(t) = 5 yı(t) = 5+40/5t45 M yz(t) = 5+8(4/5t-10+t^5) M yz(t) = 5+8t45+256^15/75+32t10/5 M (b) Find the general term cx(t) of the n-th approximation yn (t) = ) w ck(t) = Note: Do not include the factorial k! in the definition of c(t). (C) Find the exact solution to the initial value problem above as y(t) = lim yn (t), 100 y(t) = Help Entering Answers

Answer 1

Yonn = yot It(t, Yn) dt to y' (t) = 8t y(t) y(0) = 5 f(t, y) = 8thy Y10) = 5 - tozo yo = 5 you yo = 5 y = y + / flt, go) at y = 5 + tj 8t (5) dt 4:5+ 5*8* tsa 744= 5 +8651 5 Y ₂ = 4g + f(ty,)dt = 5evo + p 8+" (57875) at = 5 + 4 40 + 4 + 64 at det 3 5 & DO* + 40+ 64 to 5 To

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