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Question
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
Options
xy = C
x = Cy2
y = Cx
y = Cx2
Solution
y = Cx
We have,
\[\frac{y dx - x dy}{y} = 0\]
\[ \Rightarrow y dx = x dy\]
\[ \Rightarrow \frac{1}{y}dy = \frac{1}{x}dx\]
Integrating both sides, we get
\[\int\frac{1}{y}dy = \int\frac{1}{x}dx\]
\[ \Rightarrow \log y = \log x + D\]
\[ \Rightarrow \log y - \log x = \log C\]
\[ \Rightarrow \log\left( \frac{y}{x} \right) = \log C\]
\[ \Rightarrow \frac{y}{x} = C\]
\[ \Rightarrow y = Cx\]
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