Question

The integrating factor of the differential equation sin x(dy)/(dx)+2ycos x=1 is:

• A. \(\sin^2 x\)
• B. \(\dfrac{2}{\sin x}\)
• C. \(\log|\sin x|\)
• D. (1)/(sin² x)

Hint:

Always reduce to standard linear form before finding IF.

Answer 1

The Correct Option is A

Step 1: Write in linear form: (dy)/(dx)+2ycot x=csc x
Step 2: Integrating factor: IF=eⁱⁿᵗ ²ᶜoᵗ ˣ ᵈˣ=e²lⁿˢⁱⁿ ˣ=sin² x