Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.9 Introduction to Differential Equations - 7.9 Exercises - Page 589: 6

Answer

$${\text{The equation is separable}}$$

Work Step by Step

$$\eqalign{ & {t^2}y'\left( t \right) = \left( {t + 4} \right){y^2} \cr & {\text{Multiply both sides of the equation by }}\frac{1}{{{t^2}{y^2}}} \cr & \frac{1}{{{t^2}{y^2}}}\left[ {{t^2}y'\left( t \right)} \right] = \frac{1}{{{t^2}{y^2}}}\left[ {\left( {t + 4} \right){y^2}} \right] \cr & \frac{1}{{{y^2}}}y'\left( t \right) = \frac{1}{{{t^2}}}\left( {t + 4} \right){y^2} \cr & {\text{The d}}{\text{.e can be written in the form }}g\left( y \right)y'\left( t \right) = h\left( t \right),{\text{ then}} \cr & {\text{we can conclude that the equation is separable}}{\text{.}} \cr} $$
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