Consider the functional1Sl[y] = fShow that the function y(x), defined by the relationy'(x) = c√/1 + x + y'(x)²,where c is a constant, makes S[y] stationary. By expressing y'(x) in terms of x,solve this equation to show thatdx √1+x+y¹2, y(0)=A>0, y(1) = B > A.y(x) = A +(B - A)(23/2 - 1)((1 + + x)³/2² − 1). Consider the functional1Sl[y] = fShow that the function y(x), defined by the relationy'(x) = c√/1 + x + y'(x)²,where c is a constant, makes S[y] stationary. By expressing y'(x) in terms of x,solve this equation to show thatdx √1+x+y¹2, y(0)=A>0, y(1) = B > A.y(x) = A +(B - A)(23/2 - 1)((1 + + x)³/2² − 1).

Answered: Image /qna-images/answer/965606fe-e8da-44a1-86fb-71080847496e.jpg

Consider the functional 1 S[y] = f'da dx √1+x+y¹2, y(0)=A>0, y(1) = B > A. Show that the function y(x), defined by the relation y'(x) = c√1+x+y'(x)², where c is a constant, makes S[y] stationary. By expressing y'(x) in terms of x, solve this equation to show that y(x) = A + (B − A) (23/2 - 1) ·((1+ + x)³/² − 1).

Consider the functional 1 S[y] = f'da dx √1+x+y¹2, y(0)=A>0, y(1) = B > A. Show that the function y(x), defined by the relation y'(x) = c√1+x+y'(x)², where c is a constant, makes S[y] stationary. By expressing y'(x) in terms of x, solve this equation to show that y(x) = A + (B − A) (23/2 - 1) ·((1+ + x)³/² − 1).

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.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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