Consider the Cauchy Problem y 0 = a(x) arctan y, y(0) = 1, where a(x) is a continuous function defined on R, such that for every x it holds that |a(x)| ≤ 1. Using the Global Picard–Lindel¨of Theorem, show that there exists a unique solution y defined on R.

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A: The wronskian of f and g is given by Wf, g = f(x)g(x)f'(x)g'(x)

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A: Given: A(x)=∫0x f(x)

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A: You have correctly answered the first part. I will straightway go to the second part.

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A: Let's find.

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A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

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A: we have ut=uxx ux,0=fxux0,t=0 Fcut=Fcuxxdu¯dt=-su⇒u=Cse-s2tNow, ux,0=fx⇒us,0=f^cs=Cs⇒u=f^cse-s2t Put…

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Q: If x = c is a critical number of f, then f has a local extrema at I = c. True False

A: Question: If x=c is a critical number of f then f has a local extrema at x=c

Q: Let f (x, y) = y³ + x² – 3y (a) Determine all the critical points of f. (b) Determine the absolute…

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Q: Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and h(x, y) = 2x² + y². a) Find all the local maximum and…

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