Solve the differential equation : \(y - x\dfrac{dy}{dx} = 0\)Solution : Given equation is \(y - x\dfrac{dy}{dx} = 0\)Separating the variables we get\(\dfrac{dx}{\square} = \dfrac{dy}{\square}\)Integrating we get,\(\displaystyle\int \frac{dx}{\square}…

Q.3 (C)(ii) Solve the differential equation : \(y - x\dfrac{dy}{dx} = 0\)

Solution : Given equation is \(y - x\dfrac{dy}{dx} = 0\)

Separating the variables we get

\(\dfrac{dx}{\square} = \dfrac{dy}{\square}\)

Integrating we get,

\(\displaystyle\int \frac{dx}{\square} = \int \frac{dy}{\square} + c\)

\(\therefore \log x = \square + c\)

\(\therefore \log x - \log y = \log c_1\), where \(c = \log c_1\)

\(\therefore \log\left(\dfrac{x}{y}\right) = \log c_1\)

\(\therefore \dfrac{x}{\square} = c_1\)

Hence the required solution is \(x = c_1y\).