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 DExplanation:Given differential equation is y(1+xy)dx=xdy ⇒ydx+xy2dx=xdy ⇒xdy−ydxy2=xdx ⇒−(ydx−xdy)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