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: 17

Answer

$$y\left( t \right) = {t^3} - 2{t^2} + 10t + 20$$

Work Step by Step

$$\eqalign{ & y'\left( t \right) = 3{t^2} - 4t + 10 \cr & {\text{integrate both sides }} \cr & \int {y'\left( t \right)} = \int {\left( {3{t^2} - 4t + 10} \right)dt} \cr & y\left( t \right) = {t^3} - 2{t^2} + 10t + C \cr & {\text{the initial condition }}y\left( 0 \right) = 20{\text{ implies that}} \cr & 20 = {\left( 0 \right)^3} - 2{\left( 0 \right)^2} + 10t + C \cr & C = 20 \cr & {\text{so the solution of the initial value problem is}} \cr & y\left( t \right) = {t^3} - 2{t^2} + 10t + 20 \cr} $$
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