Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
Question
The general solution of the differential equation $\frac{y d x-x d y}{y}=0$ is
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Answer
It is given that $\frac{\mathrm{ydx}-\mathrm{xdy}}{\mathrm{y}}=0$ $\Rightarrow \frac{\mathrm{ydx}-\mathrm{xdy}}{\mathrm{xy}}=0$ $\Rightarrow \frac{1}{x} d x-\frac{1}{y} d y=0$ Integrating both sides, we get, log|x| - log|y| = log k $\Rightarrow \log \left|\frac{x}{y}\right|=\log k$ $\Rightarrow \frac{x}{y}=k$ $\Rightarrow \mathrm{y}=\frac{1}{\mathrm{k}} \mathrm{x}$ $\Rightarrow$ y = Cx where C = $\frac{1}{k}$
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