Correct Answer - Option 3 : y = c (x
2 + 1)
Calculation:
Given differential equation
\(\rm (x^2+1){dy\over dx} = 2xy\)
\(\rm {dy\over y} = {2x\over x^2+1} dx\)
Let x2 = t ⇒ 2x dx = dt
\(\rm {dy\over y} = {dt\over t+1} \)
Integrating both the sides, we get
\(\rm \int {dy\over y} =\int {dt\over t+1} \)
ln y = ln (t + 1) + ln c
ln y = ln [(x2 + 1) c] [log m + log n = log mn]
y = C (x2 + 1)