The general solution of the differential equation `dy / dx = y / x` is

Explanation

We have,
`frac{d y}{d x}=frac{y}{x} `


`Rightarrow frac{1}{y} d y=frac{1}{x} d x`


By Integrating each sides, we obtain


`int frac{1}{y} d y=int frac{1}{x} d x `


`Rightarrow log y=log x+log k `


`Rightarrow log y-log x=log k `


`Rightarrow log (frac{y}{x})=log k `


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