Consider the initial–value problem with

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the initial–value problem

\dfrac{dy}{dx}=\dfrac{1}{\sqrt{1-x^{2}}}

with

y(0)=3

. What is

y\!\left(\dfrac{1}{2}\right)

? (a)

3-\dfrac{\pi}{6}

(b)

3+\dfrac{\pi}{12}

(c)

3+\dfrac{\pi}{6}

(d)

\dfrac{\pi}{6}

Related theory

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