Question

The expression satisfying the differential equation (x²-1)dfracdydx+2xy=1 is:

• A. \(x^2y-xy^2=c\)
• B. \((y^2-1)x=y+c\)
• C. \((x^2-1)y=x+c\)
• D. none of these

Hint:

Put the DE in linear form before finding the IF.

Answer 1

The Correct Option is C

Step 1: Write as linear in y: (dy)/(dx)+(2x)/(x²-1)y=(1)/(x²-1).
Step 2: Integrating factor: IF=eⁱⁿᵗ ⁽²ˣ⁾/⁽ˣ^²⁻¹⁾ᵈˣ=x²-1.
Step 3: Hence (x²-1)y=int 1dx=x+c.