Question

An integrating factor of the differential equation xdydx+ylog⁡x=xexx−12log⁡x,(x>0)

• A. (A) xlog⁡x
• B. (B) (x)log⁡x
• C. (C) {e}{log⁡x}2
• D. (D) ex2

Answer 1

Answer: (C)

(C) {e}{log⁡x}2

Answer 2

Explanation:
Given differential equation isxdydx+ylog⁡x=xexx−1/2log⁡xdydx+y1xlog⁡x=exx−1/2log⁡x Here, P=1xlog⁡x and Q=exx−1/2log⁡x∴IF=e∫1xlog⁡xdx=e(log⁡x)22=(e)log⁡x)2