liferential equation with variable coefficients, y" + p(t)y/ + q(t)y = 0 (i), %3D can be transformed into an equation with constant coefficie change of the independent variable. Let z = u(t) = /(ate)"² dt, %3D with q(t) > 0, be the new independent variable. If the functi d (t) + 2p(t)q(t) 2(g(t))/2 H = is a constant, then (i) can be transformed into an equation wi constant coefficients by a change of the independent variable. Consider the differential equation y" + 4ty' + ty= 0. Calculate using the formula above, and then determine whether it is poss: to transform the differential equation into one with constant coefficients using this method. Choose one Yes, it is possible. No, it is not possible.
liferential equation with variable coefficients, y" + p(t)y/ + q(t)y = 0 (i), %3D can be transformed into an equation with constant coefficie change of the independent variable. Let z = u(t) = /(ate)"² dt, %3D with q(t) > 0, be the new independent variable. If the functi d (t) + 2p(t)q(t) 2(g(t))/2 H = is a constant, then (i) can be transformed into an equation wi constant coefficients by a change of the independent variable. Consider the differential equation y" + 4ty' + ty= 0. Calculate using the formula above, and then determine whether it is poss: to transform the differential equation into one with constant coefficients using this method. Choose one Yes, it is possible. No, it is not possible.
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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#3 HANDWRITTEN
Transcribed Image Text:Often a differential equation with variable coefficients,
y"+ p(t)y' + q(t)y = 0 (i),
can be transformed into an equation with constant coefficie
change of the independent variable. Let
dt,
with q(t) > 0, be the new independent variable. If the functi-
d'(t) + 2p(t)q(t)
H
2(9(t))/2
is a constant, then (i) can be transformed into an equation wia
constant coefficients by a change of the independent variable.
Consider the differential equation y"+ 4ty' +ty 0. Calculate
using the formula above, and then determine whether it is possi
to transform the differetial equation into one with constant
coefficients using this method.
Choose one
Yes, it is possible.
No, it is not possible.
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