Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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Step 2: Deriving the Riccati's equation by the transformation
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