Chapter 6 - Differential Equations - 6.3 Exercises - Page 421: 8

$y=Cx$

Begin by rewriting the differential equation $xy' = y$ $\frac{dy}{dx}=\frac{y}{x}$ $\frac{dy}{y}= \frac{dx}{x}$ Integrate both sides $\int\frac{dy}{y} = \int\frac{dx}{x}$ $ \ln{|y|}= \ln{|x|} +C$ Exponentiate using e as the base to cancel the ln's. $y= e^{ln|x| +C} $ Simplify $y=Cx$