The particular solution of the differential equation \( xdy+ydx=0 \), given \( y=2 \), when \( x=1 \), is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( xy=2 \)
The left side is an exact differential, because by the product rule \( d(xy)=x\,dy+y\,dx \).
\( \displaystyle d(xy)=0\ \Rightarrow\ xy=C \)
Put x = 1, y = 2:
\( \displaystyle C=1\times 2=2 \)
\( \displaystyle xy=2 \)