Question

The solution of the differential equation \(dx+dy=0\) is

• A. \(x=ky\)
• B. \(x^{2}+y^{2}=k\)
• C. \(x+y=k\)
• D. \(xy=k\)

Hint:

When differentials separate directly, integrate both sides and combine constants.

Answer 1

The Correct Option is C

Rewrite \(dx+dy=0\) as \(dy=-dx\). Integrate both sides: \[ \int dy=\int(-dx)\Rightarrow y=-x+C. \] Move \(x\) to the left: \(x+y=C=k\). This represents straight lines of slope \(-1\).