Question

The integrating factor of the differential equation 2ydxdy+x=5y2 is, (y≠0):

• A. (A) y
• B. (B) y2
• C. (C) y
• D. (D) 1y

Answer 1

Answer: (A)

(A) y

Answer 2

Explanation:
Given,2ydxdy+x=5y2… (i)Equation (i) can be simplified as,dx dy+x2y=52yOn comparing eqn (i) with standard eqn,dxdy+Px=Q,We getP=12y and Q=52yTherefore,IF=e∫Pdy=e∫12ydy⇒IF=e12log⁡y=elog⁡y12⇒IF=y(∵ealog⁡x=xa)Hence, the correct option is (A).