Consider the differential equation ty" + (-12t2 – 1)y' + 36t°y = 0, para t > 0. We know that the differential equation admits a solution of the form y(t) = e" for fixed r. Let y(t) be any solution to the differential equation. Regarding the behavior of the solutions regarding t → +o we can say that: a. lim t 2e-32 +3y(t) = u'(1) – 3y(1). %3D t+00 b. lim e 4+4y(t) = ty'(1) – y(1). t100 C. lim e 4t y(t) não está definido e lim e 5 y(t) = 0. 5t2 %3D t+00 t+00
Consider the differential equation ty" + (-12t2 – 1)y' + 36t°y = 0, para t > 0. We know that the differential equation admits a solution of the form y(t) = e" for fixed r. Let y(t) be any solution to the differential equation. Regarding the behavior of the solutions regarding t → +o we can say that: a. lim t 2e-32 +3y(t) = u'(1) – 3y(1). %3D t+00 b. lim e 4+4y(t) = ty'(1) – y(1). t100 C. lim e 4t y(t) não está definido e lim e 5 y(t) = 0. 5t2 %3D t+00 t+00
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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Consider the differential equation:
Transcribed Image Text:Consider the differential equation
ty" + (-12t – 1)y' + 36t°y = 0, para t > 0.
We know that the differential equation admits a solution of the form y(t) = e" for fixed r. Let
y(t) be any solution to the differential equation. Regarding the behavior of the solutions
regarding t → +o we can say that:
a. lim t 2e 32 +3y(t) = y'(1) - 3y(1).
%3D
t+00
b. lim e 4+4y(t) = ty'(1) – y(1).
t+00
c. lim e
4t y(t) não está definido e lim e
5t2
y(t) = 0.
%3D
t+00
t+00
d. lim e
312
y(t) não está definido e lim e
At y(t) = 0.
%3D
t+00
t+00
e. lim t 3e 32 +3y(t) = y'(1) – 3y(1).
t+00
f. lim e
5P 13y(t) = ty'(1) – y(1).
%3D
t+00
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