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Consider the equation d²u dx² P₂(x)- du dx + P₁(x). + po(x)u = 0. dx y By introducing a new function y(x) by u = exp (f dr. the Riccati equation dy Po P1 - y². dx P2 P2 show that Y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.

Consider the equation d²u dx² P₂(x)- du dx + P₁(x). + po(x)u = 0. dx y By introducing a new function y(x) by u = exp (f dr. the Riccati equation dy Po P1 - y². dx P2 P2 show that Y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.

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 the equation d² u du P2(x)- + P₁(x). + Po(x)u = 0. d.x dx² By introducing a new function y(x) by u = exp (f dx y) the Riccati equation dy dx Po P1 P2 -y - y². P2 show that y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.
Transcribed Image Text:Consider the equation d² u du P2(x)- + P₁(x). + Po(x)u = 0. d.x dx² By introducing a new function y(x) by u = exp (f dx y) the Riccati equation dy dx Po P1 P2 -y - y². P2 show that y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.
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