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Islder Hermites equdtion y" – 2æy + 4y = 0 and verify for yourself that y1 = 1 – 2x2 is a solution. The "reduction of order" technique for finding a second solution, y2, that is linearly independent of the first, is to set y2 = Y1v and fi non-constant v that makes yY2 ɑ solution. This yields a first order equation for w = v' of the form w' + Pw = 0. Perform this technique and find the function P that appears in the above equation. P (x) =

Islder Hermites equdtion y" – 2æy + 4y = 0 and verify for yourself that y1 = 1 – 2x2 is a solution. The "reduction of order" technique for finding a second solution, y2, that is linearly independent of the first, is to set y2 = Y1v and fi non-constant v that makes yY2 ɑ solution. This yields a first order equation for w = v' of the form w' + Pw = 0. Perform this technique and find the function P that appears in the above equation. P (x) =

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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Consider Hermite's equation of order two: y' – 2xy + 4y = 0 and verify for yourself that y1 = 1– 2x? is a solution. The "reduction of order" technique for finding a second solution, y2, that is linearly independent of the first, is to set Y2 = Y1v and find a non-constant v that makes y2 a solution. This yields a first order equation for w = v' of the form w' + Pw = 0. Perform this technique and find the function P that appears in the above equation. P (x) =
Transcribed Image Text:Consider Hermite's equation of order two: y' – 2xy + 4y = 0 and verify for yourself that y1 = 1– 2x? is a solution. The "reduction of order" technique for finding a second solution, y2, that is linearly independent of the first, is to set Y2 = Y1v and find a non-constant v that makes y2 a solution. This yields a first order equation for w = v' of the form w' + Pw = 0. Perform this technique and find the function P that appears in the above equation. P (x) =
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