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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.

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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Solve Question 4 B using Applied Analysis.

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.
Transcribed Image Text: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.
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