Question

this problem is related to thoery of diffrential equation

and u have the THR 3.43

높 (t,0,0) aa (t;o,o) and n chece your answer Saluing 8.9 Differentiating Solutions with Respect to on (t1,t2]. With properties of f ICs In this section we will be concerned with differentiating solutions with respect to initial conditions, initial points, and parameters. Theorem 8.43 (Differentiation with Respect to Initial Conditions and Initial Points) Assume f is a continuous n dimensional vector function on an open set DCR x Rn and f has continuous partial derivatives with respect to the components of x. Then the IVP (8.4), where (to, ro) E D, has a unique solution, which we denote by r(t;to, To), with marimal interval of eristence (a, w). Then (t;to, To) has continuous partial derivatives with respect to the components roj, j- 1,2,..,n of ro and with respect to to on (a,w). Furthermore, z(t)ato) defines the unique solution of the IVP it follows that for ti

Answer 1

宁(zdzi 7 b Itb

ItD ai MT 十一だ 2 デ 宁π