Page 2 : Published by :, , FIREWALL MEDIA, (An Imprint of Laxmi Publications Pot. Ltd.), 113, Golden House, Daryaganj,, , New Delhi-110002, , Phone : 011-43 53 25 00, Fax : 011-43 53 25 28, , www laxmipublications.com,
[email protected], , ISBN = 81-7008-939.-5, , Copyright © 2007 by Firewall Media (An imprint of Laxmi Publications Pot. Ltd.). 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., , , , Price : Rs, 250.00 Only., , Offices :, , India, , ‘© Bangalore (Phone : 080-26 61 15 61), , ‘© Chennai (Phone : 044-24 34 47 26), , ‘© Cochin (Phone : 0484-239 70 04), , ¢ Guwahati (Phones : 0361-254 36 69, 251 38 81), © Hyderabad (Phone : 040-24 75 02 47), , © Jalandhar City (Phone : 0181-222 12 72), , ‘¢ Kolkata (Phones : 033-22 27 37 73, 22 27 52.47), ¢ Lucknow (Phone : 0522-220 95 78), , ¢ Mumbai (Phones : 022-24 91 54 15, 24 92 78 69), © Ranchi (Phone : 0651-230 77 64), , , , ‘Tenth Edition : 2006, , USA, ‘© Boston, 11, Leavitt Street, Hingham,, ‘MA 02043, USA, Phone : 781-740-4487, , , , ‘MGA-6706-250-G. DIFF. EQUATIONS, ‘Typeset at : Goswami Printers, Delhi., , C—13019/06/08, Printed at : Sanjeev Offset Press, New Delhi.
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Chapters Pages, List of Important Formulae (i)}—Wwi), 1._Differential Equations and their Formation a, 2._ Solution of Differential Equations of the First Order and First Degree. 21, 8.__Linear Equations with Constant Co-efficients a 170, 4. Application to Geometry and Mechanics a), 5. Homogeneous Linear Equations 286, °6._Trajectories cS, 7, Equations of the First Order but not of the First Degree 326, 8.__Linear Equations of Second Order. 356, 9._ Simultaneous Differential Equations 400, 10.__ Series Solution of Differential Equations 429, I1._Legendre’s Ei 512, 12._Bessel’s Equation 22 533, , , , , , sschiltztes Material
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GET 100 OUT OF 100 MARKS, , ‘The book has been written with a view to guide the, students in the examination. It ensures 100% marks, , ‘The student is advised to take this book only as, a help book. He should solve himself as, many questions as possible., , "= Special Features :, 1, Solutions to all types of important questions have been given., 2, Questions from up-to-date papers of various Universities., 8, The book is useful to bright as well as weak students alike., 4. Approach to the subject matter is systematic., 5, The Book serves triple purpose :, ‘Text Book—Help Book—Solved University Papers
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List of Important Formulae, , (T0 BE LEARNT BY HEART], 1 VARIABLES SEPARABLE, , ‘To solve $Y = XY, where X is a function of x only and ¥ is a function of y only., , Bring all the terms of x and dx on one side, all the terms of y and dy on the other., Integrate both sides and add an abritrary constant on one side., , 2. HOMOGENEOUS EQUATION, , To solve the equation 2 ae . where f(x, y), fx, y) are homogeneous funeae,, , tions of the same degree in x and y., , ay do, re, so that 7 ate a, , , , Puty, , , , ‘Substitute the values of y and * in the given equation., , Separate the variables v and x., Integrate both sides and add an arbitrary constant on one side., , Substitute back the value of v (- x), , 8. EQUATIONS REDUCIBLE TO HOMOGENEOUS, . dy _axtbyte, (To solve = Seah y te ', Putx=X+hyaYok, , Equate the constant terms in the numerator and denominator of R.H.S. to zero and find, hand k., , ‘The equation is now homogeneous in X and Y., , Put Y = oX and proceed as in the case of homogeneous equations. Substitute back the, values of v, X, Y, A and k., , , , o
