Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Thus, with , the period of . Further simplification arises from imposing the inert initial contitions.
Maple can return the expression for as a fraction containing either or .
The replacement of the negative exponential with is crucial for the next step, a Taylor expansion in powers of the negative exponential. A graph of this version of the solution, namely is given in Figure 10.25, where, on the interval , the solution is exact because is zero, since . If that term had been retained, and inverted, it would have contributed a multiple of , and this term is zero for . We next obtain a sequence of approximate solutions which rapidly converge to the exact solution. In the differential equation, the driving function is replaced by , a partial sum of the Fourier series of , and the corresponding solution computed.