Question

For the primitive integral equation ydx + y²dy = xdy, x ∈ R, y > 0, y = y (x), y(1) = 1, then y(– 3) is 

(a) 3 

(b) 2 

(c) 1 

(d) 5

Answer 1

Answer is (a) 3

Explanation:

The given differential equation is

ydx + y² = xdy

ydx – xdy = – y²dy

When x = 1, y =1, then c = 2

Thus, the equation of the curve is 

y² – 2y – 3 = 0

(y – 3)(y + 1) = 0

y = 3, –1

Since y > 0, so the value of y = 3.