Solve the following initial value problems (a) u ' 3u ex, u(1) 0 (b) u 4u 1, u() u '() 0 (c) u u ' 2u ex e x, u(0) u '(0) 0 (d) u 2u 5u sin x, u(0) 1, u '(0) 0 (e) u u u ' u x, u(0) 0, u '(0) 1, u (0) 0

Question: Solve the following initial value problems: (a) u' + 3u = ex, u(1) = 0 (b) u + 4u = 1, u() = u'() =

Solve the following initial value problems:
(a) u' + 3u = ex, u(1) = 0
(b) u" + 4u = 1, u(π) = u'(π) = 0
(c) u" - u' - 2u = ex + e-x, u(0) = u'(0) = 0
(d) u" + 2u′ + 5u = sin x, u(0) = 1, u'(0) = 0
(e) u‴ - u" + u' - u = x, u(0) = 0, u'(0) = 1, u"(0) = 0

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