## Calculus with Applications (10th Edition)

$${\text{No linear}}{\text{, No separable}}$$
\eqalign{ & \frac{{dy}}{{dx}} = {x^2} + {y^2} \cr & {\text{subtract }}{y^2}{\text{ from each side}} \cr & \frac{{dy}}{{dx}} - {y^2} = {x^2} \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}} = {x^2} + {y^2} \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}