Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (1), can be transformed into an equation with constant coefficients by a change of the independent variable. Let x = u(t) dt, %3D with q(t) > 0, be the new independent variable. If the function d (t) + 2p(t)q(t) 2(q(t))³/2 H || is a constant, then (i) can be transformed into an equation with constant coefficients by a change of the independent variable. Consider the differential equation y" + 8ty' +t²y= 0. Calculate H using the formula above, and then determine whether it is possible to transform the differential equation into one with constant coefficients using this method. H Choose one

Advanced Engineering Mathematics
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Often a differential equation with variable coefficients,
y" + p(t)y' + q(t)y = 0
(1),
can be transformed into an equation with constant coefficients by a
change of the independent variable. Let
x = u(t)
dt,
%3D
with q(t) > 0, be the new independent variable. If the function
d (t) + 2p(t)q(t)
2(q(t))³/2
H
||
is a constant, then (i) can be transformed into an equation with
constant coefficients by a change of the independent variable.
Consider the differential equation y" + 8ty' +t²y= 0. Calculate H
using the formula above, and then determine whether it is possible
to transform the differential equation into one with constant
coefficients using this method.
H
Choose one
Transcribed Image Text:Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (1), can be transformed into an equation with constant coefficients by a change of the independent variable. Let x = u(t) dt, %3D with q(t) > 0, be the new independent variable. If the function d (t) + 2p(t)q(t) 2(q(t))³/2 H || is a constant, then (i) can be transformed into an equation with constant coefficients by a change of the independent variable. Consider the differential equation y" + 8ty' +t²y= 0. Calculate H using the formula above, and then determine whether it is possible to transform the differential equation into one with constant coefficients using this method. H Choose one
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