A continuously differentiable function ϕ(x),x∈[0,π]−{π2} satisfying y′=1+y2,y(0)=0=y(π) is

tanx

x(x−π)

(x−π)(1−ex)

sec2x

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A continuously differentiable function ϕ(x),x∈[0,π]−{π2} satisfying y′=1+y2,y(0)=0=y(π) is

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Text solutionVerified

[a] Given dydx=1+y2 ⇒dy1+y2=dx⇒tan−1y=x+c ⇒y=tan(x+c), now y(0)=0⇒tanc=0 y(π)=0⇒tan(π+c)=0⇒c=nπ ∴y=tanx

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Question Text	A continuously differentiable function ϕ(x),x∈[0,π]−{π2} satisfying y′=1+y2,y(0)=0=y(π) is
Answer Type	Text solution:1
Upvotes	150