Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - 6.3 Exercises: 8

Answer

$y=Cx$

Work Step by Step

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 $y=Cx$
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