Consider the i.v.p X = +2 + Cos(x), Xal = 0. Vevity that the hypotheses of Cauchy Picard theorem for a suitable domatin D 1) fltix)=t²+ Cosa is Continuous vt and x as both t² and cosix) are continuous functions. 2) To check the Lipschitz Condition with respect tox, we compute the partial derivative of fitx) with respect to x. df -Sinc This derivative is bounded VX which means fltix) Satisfies a Lipschizz Condition with respect tox. The hypothesis of the Cauchy Picard thearem is satisfied for the inital Value problem on Some domam D avound t=0. B Then estimate the interval of existence of the Soln.

Consider the i.v.p X = +2 + Cos(x), Xal = 0. Vevity that the hypotheses of Cauchy Picard theorem for a suitable domatin D 1) fltix)=t²+ Cosa is Continuous vt and x as both t² and cosix) are continuous functions. 2) To check the Lipschitz Condition with respect tox, we compute the partial derivative of fitx) with respect to x. df -Sinc This derivative is bounded VX which means fltix) Satisfies a Lipschizz Condition with respect tox. The hypothesis of the Cauchy Picard thearem is satisfied for the inital Value problem on Some domam D avound t=0. B Then estimate the interval of existence of the Soln.

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.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 4CR

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