Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 17 - Second-Order Differential Equations - Review - True-False Quiz - Page 1221: 4



Work Step by Step

$y_{p}=Ae^{x}$ $y_{p}'=Ae^{x}$ $y_{p}''=Ae^{x}$ Substitute equations in the differential equation to get $(Ae^{x})-(Ae^{x})=e^{x}$ $0=e^{x}$ Which is not true, therefore the particular solution is not of the form $y_{p}=Ae^{x}$ Remember that if the sum of the coefficients of a differential equation is zero and $G(x)=e^{kx}P(x)$, then $y_{p}$ is of the form $xQ(x)e^{kx}$ Where P(x) and Q(x) are polynomials of the same degree The sum of coefficients of the given differential equation is $1+0-1=0$ Therefore, the particular solution is of the form $y_{p}=xAe^{x}$
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