Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 83



Work Step by Step

The anti-derivative for $\dfrac{d^2y}{dx^2}=2-6x$ is $\dfrac{dy}{dx}=2x-3x^2+c$ and $y=x^2-x^3+cx+c'$ Now, apply Initial conditions $y'(0)=4 ; y(0)=1$, we have This implies, $0-0+c=4$ and $0+c'=1 \implies c'=1$ Hence, $y=x^2-x^3+4x+1$
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