Consider the initial value problem y'(t) = f (t)y(t), y(0) = 1 where f: R → R is continuous. Then this initial value problem has (a) Infinitely many solutions for some f (b) A unique solution in R (c) No solution in R for some f (d) A solution in an interval containing 0, but not on R for some f
Consider the initial value problem y'(t) = f (t)y(t), y(0) = 1 where f: R → R is continuous. Then this initial value problem has (a) Infinitely many solutions for some f (b) A unique solution in R (c) No solution in R for some f (d) A solution in an interval containing 0, but not on R for some f
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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solve both ,plz fast its urgent
Transcribed Image Text:The general solution of the differential
equation dy+
+y = f(x), xe(-∞, ∞), where
dx?
f is a continuous, real-valued function on
(-00, 00), is (where A, B, C and k are arbitrary
constants)
(a)
y(x) = Acos x +Bsinx+ f(t) sin(x-t) dt
%3D
(b)
y(x) = cos (x + k)+C[ƒ(t)sin(x – t) dt
f (t) sin(x - t) dt
(c)
y(x) = A cos x+B sinx + ƒ(x-t)sint dt
(d)
y(x) = Acos x+Bsin x + ƒ(x+t)cost dt
Transcribed Image Text:Consider the initial value problem
y'(t) = f (t)y(t), y(0) = 1
where f: R → R is continuous.
Then this initial value problem has
(a)
Infinitely many solutions for some f
(b)
A unique solution in R
(c)
No solution in R for some f
(d)
A solution in an interval containing 0,
but not on R for some f
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