Differential Equations 2 Question 15

15. If a curve y=f(x) passes through the point (1,1) and satisfies the differential equation, y(1+xy)dx=xdy, then f12 is equal to

(a) 25

(b) 45

(c) 25

(d) 45

(2016 Main)

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Answer:

Correct Answer: 15. (d)

Solution:

  1. Given differential equation is

y(1+xy)dx=xdyydx+xy2dx=xdyxdyydxy2=xdx(ydxxdy)y2=xdxdxy=xdx

On integrating both sides, we get

xy=x22+C

It passes through (1,1).

1=12+CC=12

Now, from Eq. (i) xy=x22+12

x2+1=2xyy=2xx2+1f12=45



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