The solution of the differential equation \( (x-1)\displaystyle\frac{dx}{dy}+(y-2)=0 \), given \( x=1,y=1 \) represents a
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Circle
Multiplying by dy, the variables separate:
\( (x-1)\,dx+(y-2)\,dy=0 \)
Integrating:
\( \displaystyle \frac{(x-1)^2}{2}+\frac{(y-2)^2}{2}=k \)
\( (x-1)^2+(y-2)^2=C \)
At (1, 1): C = 0 + 1 = 1. So the solution is \( (x-1)^2+(y-2)^2=1 \), a circle with centre (1, 2) and radius 1.