Let function $$y=f(x)$$ satisfies the differential equation $$x2dydx=y2e1x(x$$≠$$0)$$ and limx→$$0f(x)=1$$ . Identity the correct statements?

Correct option is 1,2,4undefined

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$Let function y = f (x) satisfies the differential equation x^{2} \frac{d y}{d x} = y^{2} e^{\frac{1}{x}} (x \neq 0) and$ $\lim_{x \to 0} f (x) = 1 . Identity the correct statements?$

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Range of f(x) is (0,1)-12

f(x) is bounded

limx→±∞fx=1

∫0efxdx>∫01fxdx

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detailed solution

Correct option is A

dyy2=e1xx2dx⇒-1y=-∫etdt+cput1x=t⇒-1y=-e1x+c∴limx→0f(x)=1⇒-1=0+c⇒c=-1∴y=11+e1xlimx→∞11+e1x=12

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Let function y=f(x) satisfies the differential equation x2dydx=y2e1x(x≠0) and limx→0f(x)=1 . Identity the correct statements?

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$Let function y = f (x) satisfies the differential equation x^{2} \frac{d y}{d x} = y^{2} e^{\frac{1}{x}} (x \neq 0) and$ $\lim_{x \to 0} f (x) = 1 . Identity the correct statements?$