Question:
The solution of the differential equation \(dx+dy=0\) is
The solution of the differential equation \(dx+dy=0\) is
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When differentials separate directly, integrate both sides and combine constants.
Updated On: Oct 15, 2025
- \(x=ky\)
- \(x^{2}+y^{2}=k\)
- \(x+y=k\)
- \(xy=k\)
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The Correct Option is C
Solution and Explanation
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 \(-1\).
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