If yı is a known nonvanishing solution of y" + p(t)y' + q(t)y = 0, then a second solution y2 satisfies Y2 W[y1, Y2] The solution y2 can be found using Abel's formula, || Y1 which states that if y1 and y2 are solutions to y" + p(t)y' + q(t) = 0, q are continuous on an open interval I, then the where and Wronskian W[y1, Y2](t) is given by W[y1, Y2](t) = ce S p(t) dt. Use this result to find a second independent solution of the equation ty" + 19ty + 17y = 0, t> 0, yı(t) = t-1 NOTE: Do not write constants of integration. Your expression for the second solution ya must contain a single term which is linearly independent of yı. Based on Abel's identity: W [y1, Y2] = C1• Therefore, y2(t)
If yı is a known nonvanishing solution of y" + p(t)y' + q(t)y = 0, then a second solution y2 satisfies Y2 W[y1, Y2] The solution y2 can be found using Abel's formula, || Y1 which states that if y1 and y2 are solutions to y" + p(t)y' + q(t) = 0, q are continuous on an open interval I, then the where and Wronskian W[y1, Y2](t) is given by W[y1, Y2](t) = ce S p(t) dt. Use this result to find a second independent solution of the equation ty" + 19ty + 17y = 0, t> 0, yı(t) = t-1 NOTE: Do not write constants of integration. Your expression for the second solution ya must contain a single term which is linearly independent of yı. Based on Abel's identity: W [y1, Y2] = C1• Therefore, y2(t)
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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![If yı is a known nonvanishing solution of
y" + p(t)y' + q(t)y = 0, then a second solution y2 satisfies
Y2
W[y1, Y2]
The solution y2 can be found using Abel's formula,
||
Y1
which states that if y1 and y2 are solutions to y" + p(t)y' + q(t) = 0,
q are continuous on an open interval I, then the
where
and
Wronskian W[y1, Y2](t) is given by W[y1, Y2](t) = ce S p(t) dt.
Use this result to find a second independent solution of the equation
ty" + 19ty + 17y = 0, t> 0, yı(t) = t-1
NOTE: Do not write constants of integration. Your expression for the second
solution ya must contain a single term which is linearly independent of yı.
Based on Abel's identity:
W [y1, Y2] = C1•
Therefore, y2(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56945fae-aeca-4f60-8c3d-a266c334f238%2F1c8cb3fc-2ebc-4faf-8398-2faca14c1530%2F3rl7zhr_processed.png&w=3840&q=75)
Transcribed Image Text:If yı is a known nonvanishing solution of
y" + p(t)y' + q(t)y = 0, then a second solution y2 satisfies
Y2
W[y1, Y2]
The solution y2 can be found using Abel's formula,
||
Y1
which states that if y1 and y2 are solutions to y" + p(t)y' + q(t) = 0,
q are continuous on an open interval I, then the
where
and
Wronskian W[y1, Y2](t) is given by W[y1, Y2](t) = ce S p(t) dt.
Use this result to find a second independent solution of the equation
ty" + 19ty + 17y = 0, t> 0, yı(t) = t-1
NOTE: Do not write constants of integration. Your expression for the second
solution ya must contain a single term which is linearly independent of yı.
Based on Abel's identity:
W [y1, Y2] = C1•
Therefore, y2(t)
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