Answer
$$y =cx$$
Work Step by Step
Given $$\frac{dy}{dx}=\frac{y}{x} $$
Separate variables
\begin{align*}
\int \frac{dy}{y}&=\int \frac{dx}{x}\\
\ln y&=\ln x+\ln c\\
&=\ln cx\\
y&=cx
\end{align*}
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 8 - Mathematical Modeling With Differential Equations - 8.2 Separation Of Variables - Exercises Set 8.2 - Page 575: 1
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