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Consider the following Differential Equation (Riccati Equation): y' = p(x) + q(x)y+r(x)y² If u is a solution of the given DE, use the transformation: 1 y = u +- v Prove that the solution of the DE: d k dx 1 + (y')², is a circle equation considering that k is a constant. Then, find the center and radius of this circle given that y(-1) = y(1) = 0

Consider the following Differential Equation (Riccati Equation): y' = p(x) + q(x)y+r(x)y² If u is a solution of the given DE, use the transformation: 1 y = u +- v Prove that the solution of the DE: d k dx 1 + (y')², is a circle equation considering that k is a constant. Then, find the center and radius of this circle given that y(-1) = y(1) = 0

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 following Differential Equation (Riccati Equation): y' = p(x) + q(x)y+r(x)y² If u is a solution of the given DE, use the transformation: 1 y = u +- v Prove that the solution of the DE: d k dx 1 + (y')², is a circle equation considering that k is a constant. Then, find the center and radius of this circle given that y(-1) = y(1) = 0
Transcribed Image Text:Consider the following Differential Equation (Riccati Equation): y' = p(x) + q(x)y+r(x)y² If u is a solution of the given DE, use the transformation: 1 y = u +- v Prove that the solution of the DE: d k dx 1 + (y')², is a circle equation considering that k is a constant. Then, find the center and radius of this circle given that y(-1) = y(1) = 0
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