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5. Given that y =c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (- 00,00), show that constants c, and c, cannot be found so that a member of the family satisfies the initial conditions y(0)= 0, y'(0)=1. Explain why this does not violate Theorem 4.1.1.

5. Given that y =c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (- 00,00), show that constants c, and c, cannot be found so that a member of the family satisfies the initial conditions y(0)= 0, y'(0)=1. Explain why this does not violate Theorem 4.1.1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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5. Given that y = c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (-00,00), show that constants c, and c, cannot be found so that a member of the family satisfies the initial conditions y(0) = 0, y'(0) =1. Explain why this does not violate Theorem 4.1.1.
Transcribed Image Text:5. Given that y = c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (-00,00), show that constants c, and c, cannot be found so that a member of the family satisfies the initial conditions y(0) = 0, y'(0) =1. Explain why this does not violate Theorem 4.1.1.
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