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Q.

 Let function y=f(x) satisfies the differential equation x2dydx=y2e1x(x0) and limx0f(x)=1 . Identity the correct statements? 

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a

 Range of f(x) is (0,1)-12

b

f(x) is bounded 

c

limx±fx=1

d

0efxdx>01fxdx

answer is A, B, D.

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Detailed Solution

dyy2=e1xx2dx

-1y=-etdt+cput1x=t

-1y=-e1x+c

limx0f(x)=1-1=0+cc=-1

y=11+e1x

limx11+e1x=12

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