Question

Solution of x(dy/dx) + y - x + xycotx = 0 (x ≠ 0) is

(A) xy = c/sinx + 1 - xcostx

(B) xy = csinx + xcotx

(C) xysinx = c - cotx

(D) ysinx = cx - xcotx

Answer 1

Answer is (A) xy = c/sinx + 1 - xcostx

We have

x(dy/dx) + (1 + xcotx)y = x

⇒ dy/dx + ((1 + xcotx)/x)y = 1

Therefore,

P = (1 + xcotx)/x, Q = 1

The integrating factor is

Therefore, the solution is