Q.Solve $\dfrac{dy}{dx}=\dfrac{y}{x}$.

Separating the $x$ and $y$ terms onto opposite sides and integrating each independently gives the general solution.

Separating the variables

Integrating both sides

Simplifying

Exponentiating: $|y|=e^C|x|$; writing $k=\pm e^C$ as a single arbitrary constant gives $y=kx$. …

Leaving the solution as $\ln|y|=\ln|x|+C$ without simplifying to the explicit form $y=kx$ — a differential equation's 'solution' should expre …