For the equation ay" + by' + cy = 0, if b2 – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minute Which of the following equations does it reduces to? au" + 2bu' -u + cu = 0 2a àu" – 2bu' +u + cu= 0 au" = 0 au" + 2bu' + u + cu = 0 O O O

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the equation ay" + by' + cy = 0, if b² – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is
Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of
Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minutes)
Which of the following equations does it reduces to?
au" + 2bu' - u + cu = 0
2a
62
àu" – 2bu' +u + cu = 0
au" = 0
au" + 2bu' + Eu + cu = 0
O O O
Transcribed Image Text:For the equation ay" + by' + cy = 0, if b² – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minutes) Which of the following equations does it reduces to? au" + 2bu' - u + cu = 0 2a 62 àu" – 2bu' +u + cu = 0 au" = 0 au" + 2bu' + Eu + cu = 0 O O O
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