## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter 10 - Differential Equations - Chapter Review - Review Exercises - Page 561: 17

#### Answer

$${\text{No linear}}{\text{, No separable}}$$

#### Work Step by Step

\eqalign{ & y\frac{{dy}}{{dx}} = 2x + y \cr & {\text{subtract }}y{\text{ from each side}} \cr & y\frac{{dy}}{{dx}} - y = 2x \cr & \frac{{dy}}{{dx}} - 1 = \frac{{2x}}{y} \cr & \frac{{dy}}{{dx}} - \frac{{2x}}{y} = 1 \cr & {\text{The equation cannot be written in the form }}\frac{{dy}}{{dx}} + P\left( x \right)y = Q\left( x \right)\,\,\,\left( {{\text{linear form}}} \right), \cr & {\text{ then}}{\text{, the given equation is not linear}} \cr & \cr & and \cr & \frac{{dy}}{{dx}} = \frac{{2x + y}}{y} \cr & {\text{The equation can be written in the form }}\frac{{dy}}{{dx}} = \frac{{p\left( x \right)}}{{q\left( y \right)}},{\text{ then}} \cr & {\text{the given equation is not separable}} \cr & \cr & {\text{No linear}}{\text{, No separable}} \cr}

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