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O Extend the method to a variable-coefficient ODE + p2(x)y" + P1(x)y' + po(x)y = 0. Assuming a solution yi to be known, show that another solution is y2(x) = u(x)y1(x) with u(x) = z obtained by solving Sz(x) dx and %3D yız" + (3yi + p2yı)z' + (3yi + 2p2yí + p1y1)z = 0. b) x3y" - 3x2y" + (6 – x³>xy' – (6 – x)y = 0, Reduce using v, = x (perhans obtainable bv inspection).

O Extend the method to a variable-coefficient ODE + p2(x)y" + P1(x)y' + po(x)y = 0. Assuming a solution yi to be known, show that another solution is y2(x) = u(x)y1(x) with u(x) = z obtained by solving Sz(x) dx and %3D yız" + (3yi + p2yı)z' + (3yi + 2p2yí + p1y1)z = 0. b) x3y" - 3x2y" + (6 – x³>xy' – (6 – x)y = 0, Reduce using v, = x (perhans obtainable bv inspection).

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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O12) Extend the method to a variable-coefficient ODE y" + p2(x)y" + P1(x)y' + Po(x)y = 0. Assuming a solution y1 to be known, show that another solution is y2(x) = u(x)y1(x) with u(x) = Sz(x) dx and z obtained by solving yız" + (3yi + p2yı)z' + (3y + 2p2yí + p1y1)z = 0. Reduce y" – 3x2y" + (6 – x2)xy' – (6 – x2)y = 0, %3D | using vi = x (perhaps obtainable bv inspection).
Transcribed Image Text:O12) Extend the method to a variable-coefficient ODE y" + p2(x)y" + P1(x)y' + Po(x)y = 0. Assuming a solution y1 to be known, show that another solution is y2(x) = u(x)y1(x) with u(x) = Sz(x) dx and z obtained by solving yız" + (3yi + p2yı)z' + (3y + 2p2yí + p1y1)z = 0. Reduce y" – 3x2y" + (6 – x2)xy' – (6 – x2)y = 0, %3D | using vi = x (perhaps obtainable bv inspection).
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