Use Taylors method of order two to approximate the solution for each of the following initial value problems. a. y = 2 2ty t2 + 1 , 0 t 1, y(0) = 1, with h = 0.1 b. y = y2 1 + t , 1 t 2, y(1) = (ln 2)1, with h = 0.1 C c. y = (y2 + y)/t, 1 t 3, y(1) = 2, with h = 0.2 d. y = ty + 4t/y, 0 t 1, y(0) = 1, with h = 0.1 7

M303 Section 4.3 Notes- Bases of Subspaces 11-2-16 Spanning sets give explicit description of a space, but can have redundancy o Linearly independent set will not have redundancies As in chapter 1, nonempty se{ ,,…, } of vectors in vector space is linearly independent if only solution to 1 + 2 + ⋯+ is trivial solution (all = 0) o Otherwise, set linearly dependent; dependence relation on the occurs when at least one ≠ 0 o For any , set linearly dependent iff = ; ,}linearly depe