Consider the differential equation zy" – v = (1) Making the changes of variable * = e', y = u(t)e 2* in the differential equation (1), we obtain the differential equation, u depending on t, u" – 6u' – bu = 0. The solution of the differential equation (1), depending on the parameter t, with constant c, and C2, is given by: a) { 2(t) y(t) ´z(t) et et (c1 cos(tv/15) + c2 sen(t/15)) %3D S¤(t) b) et y(t) ´z(t) c) y(t) et e3 d) { 2(t) l y(t) S¤(t) et et (c1 cos(t/15) + c2 sen(t/15)) || ||
Consider the differential equation zy" – v = (1) Making the changes of variable * = e', y = u(t)e 2* in the differential equation (1), we obtain the differential equation, u depending on t, u" – 6u' – bu = 0. The solution of the differential equation (1), depending on the parameter t, with constant c, and C2, is given by: a) { 2(t) y(t) ´z(t) et et (c1 cos(tv/15) + c2 sen(t/15)) %3D S¤(t) b) et y(t) ´z(t) c) y(t) et e3 d) { 2(t) l y(t) S¤(t) et et (c1 cos(t/15) + c2 sen(t/15)) || ||
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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(Please solve by hand)

Transcribed Image Text:Consider the differential equation
ry" - y =-
14y
* = et, y = u(t)e
2t
Making the changes of variable
in the differential equation (1), we obtain
the differential equation, u depending on t,
u" – bu' – bu = 0.
The solution of the differential equation (1), depending on the parameter t, with constant c, and
C2, is given by:
S¤(t)
el
a)
y(t)
et (c1 cos(t/15) + c2 sen(tv/15))
S2(t)
b)
et
3(t) = e (cieviB .
´z(t)
c)
y(t)
et
est
S¤(t)
= et
d)
y(t)
e* (c1 cos(tv/15) + c2 sen(t/15))
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