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If Y1 is a known nonvanishing solution of y" + p(t)y' + q(t)y = 0, then %3D Y2 a second solution y2 satisfies W (y1, Y2) where W (y1, Y2) is yi the Wronskian of y1 and y2. To determine y2, use Abel's formula, W (y1, Y2)(t) = c · e-S p()dt, where c is a certain constant that depends = c·e on yi and Y2, but not on t. Use the method above to find a second independent solution of the equation ty" – y/ + 5t°y = 0, t > 0; y1(t) = sin(t²).

If Y1 is a known nonvanishing solution of y" + p(t)y' + q(t)y = 0, then %3D Y2 a second solution y2 satisfies W (y1, Y2) where W (y1, Y2) is yi the Wronskian of y1 and y2. To determine y2, use Abel's formula, W (y1, Y2)(t) = c · e-S p()dt, where c is a certain constant that depends = c·e on yi and Y2, but not on t. Use the method above to find a second independent solution of the equation ty" – y/ + 5t°y = 0, t > 0; y1(t) = sin(t²).

Advanced Engineering Mathematics
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 yi is a known nonvanishing solution of y" + p(t)y' + q(t)y= 0, then W (y1, Y2) Y2 a second solution y2 satisfies Y1 where W (y1, Y2) is the Wronskian of y1 and y2. To determine y2, use Abel's formula, W (y1, Y2)(t) = c.eJp})dt, where c is a certain constant that depends on yi and Y2, but not on t. Use the method above to find a second independent solution of the equation ty" – y' + 5t°y = 0, t > 0; y1(t) = sin(r²). - Y2(t)
Transcribed Image Text:If yi is a known nonvanishing solution of y" + p(t)y' + q(t)y= 0, then W (y1, Y2) Y2 a second solution y2 satisfies Y1 where W (y1, Y2) is the Wronskian of y1 and y2. To determine y2, use Abel's formula, W (y1, Y2)(t) = c.eJp})dt, where c is a certain constant that depends on yi and Y2, but not on t. Use the method above to find a second independent solution of the equation ty" – y' + 5t°y = 0, t > 0; y1(t) = sin(r²). - Y2(t)
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