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1)

 If curve y=f(x) passes through the point (1,-1) and satisfies the differential equation

y(1+xy)dx=xdy , then f(-1/2) is equal to 


A) 25

B) 45

C) 25

D) 45

Answer:

Option D

Explanation:

Given  differential equation is 

y(1+xy)dx=xdy

ydx+xy2dx=xdy

xdyydxy2=xdx

(ydxxdy)y2=xdx

d(xy)=xdx

 On  integrating  both sides , we get

xy=x22+C

 It passes through(1,-1)

1=12+C

C=12

Now, from (i)

xy=x22+12

x2+1=2xy

y=x22x+1

f(12)=45