We know that y₁(x) x5 j equation 2y" + vay' - is a solution to the differential vy - u for(u,). Use the method of reduction of order to find a second solution to x²y + 5xy' — 45y = 0 for x = (0, ∞). - (a) After you reduce the second order equation by making the substitution z = u', you get a first order equation of the form 2 = f(x, z) = = Note: Make sure you use a lower case z, (and don't use z(t), it confuses the computer). y₂(x) = (b) A second solution to x²y" + 5xy' — 45y = 0 for x = (0, ∞) is =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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We know that y₁(x) x5 is a solution to the differential
=
2
equation ²y" + Jay'
лут
4jy
il = \u, wj. Use
the method of reduction of order to find a second
solution to x²y + 5xy' − 45y = 0 for x = (0, ∞).
لندن
-
(a) After you reduce the second order equation by
making the substitution z = u', you get a first order
equation of the form
z = f(x, z) =
Y₂(x) =
for
Note: Make sure you use a lower case z, (and don't use
z(t), it confuses the computer).
=
(b) A second solution to x²y" + 5xy' — 45y = 0 for
x = (0, ∞) is
Transcribed Image Text:We know that y₁(x) x5 is a solution to the differential = 2 equation ²y" + Jay' лут 4jy il = \u, wj. Use the method of reduction of order to find a second solution to x²y + 5xy' − 45y = 0 for x = (0, ∞). لندن - (a) After you reduce the second order equation by making the substitution z = u', you get a first order equation of the form z = f(x, z) = Y₂(x) = for Note: Make sure you use a lower case z, (and don't use z(t), it confuses the computer). = (b) A second solution to x²y" + 5xy' — 45y = 0 for x = (0, ∞) is
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