16: Let f(t,x) be piecewise continuous in rand Lipschitz in x on [t,,t,]x W with a Lipschitz constant L, where WcR"is . Let y(t) and z(t) be solutions of ý = f(t, y), y(t,)= Yo, 2= f(, 2) + g(t,z), z(t,) = Z,, such that y(t), z(t) eW,Vte[t,,t,]. Suppose that g(t, x)|| < µ, V(t,x)E[t,.t,]× W, for some u>0. |yM)– z(1)|| <|y,- z.|exp[L(t,-t,)]+texp[L(t,-t,)-1}, Vtet,t,). (a) an open connected set. (b) an open set. (c) convex set.
16: Let f(t,x) be piecewise continuous in rand Lipschitz in x on [t,,t,]x W with a Lipschitz constant L, where WcR"is . Let y(t) and z(t) be solutions of ý = f(t, y), y(t,)= Yo, 2= f(, 2) + g(t,z), z(t,) = Z,, such that y(t), z(t) eW,Vte[t,,t,]. Suppose that g(t, x)|| < µ, V(t,x)E[t,.t,]× W, for some u>0. |yM)– z(1)|| <|y,- z.|exp[L(t,-t,)]+texp[L(t,-t,)-1}, Vtet,t,). (a) an open connected set. (b) an open set. (c) convex set.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the following
![16: Let f(t,x) be piecewise continuous in tand Lipschitz in x on [t,t,]x W with a
Lipschitz constant L, where Wc R" is . . Let y(t) and z(t)be solutions of
ý = f(t, y), y(t,)= Y,,
ż = f(t, z) + g(t,z), z(t,) = zo,
such that y(t), z(t) e W ,Vte[t,,!,].
Suppose that g(t,x)|| < µ, V(t,x)E[t,,t,]x W, for some u>0.
|ly©) - z(0|<]y.- z.|lexp[L(t,-t,)] +texp[L(t,-t))-1}, Vte[t,t,].
(a) an open connected set.
(b) an open set.
(c) convex set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff471cf9d-9ac2-403f-8530-e1bab7d1b8d8%2F1725fd2a-d8a2-4845-8d1b-42a7abc4e905%2F8j3g3rr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:16: Let f(t,x) be piecewise continuous in tand Lipschitz in x on [t,t,]x W with a
Lipschitz constant L, where Wc R" is . . Let y(t) and z(t)be solutions of
ý = f(t, y), y(t,)= Y,,
ż = f(t, z) + g(t,z), z(t,) = zo,
such that y(t), z(t) e W ,Vte[t,,!,].
Suppose that g(t,x)|| < µ, V(t,x)E[t,,t,]x W, for some u>0.
|ly©) - z(0|<]y.- z.|lexp[L(t,-t,)] +texp[L(t,-t))-1}, Vte[t,t,].
(a) an open connected set.
(b) an open set.
(c) convex set.
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