Place each of the following linear systems in the form (7.42). Carefully describe the linear function, its domain space, its target space, and the right hand side of the system. Which systems are homogeneous?
(a) 3x + 5 = 0
(b) x = y + z
(c) a = 2b - 3, b = c - 1
(d) 3(p - 2) = 2(q - 3), p + q = 0
(e) u€² + 3xu = 0
(f) u€² + 3x = 0
(g) u€² = u, u(0) = 1
(h) u" - u = ex, u(0) = 3u(l)
(i) u" + x2u = 3x, u(0) = 1, u€²(0) = 0
(j) u' = v, v€² = 2u
(k) u" - v" = 2u - v, u(0) = u(0), u(1) = v(l)
(l)

(m)

(n)

(o)

(p)

(q)

(r)

Transcribed Image Text:

u(x) = 1-3 11(y) dy 0 a(x) dx = u(j) 0 u(y) dyy v(y)dy Ju 0 au au 2 2 ax au a aav