To determine The general solution of linear ordinary differential equation ( D 2 + 4 π D + 4 π 2 I ) y = 0 . Explanation Result used: The general solution of ordinary differential equation: “Suppose that, the linear ordinary differential equation of the form y ″ + a y ′ + b y = 0 . The auxiliary equation is m 2 + a m + b = 0 . Then, then the general solution of the equation is of the form: Case 1: If the roots are real distinct m 1 and m 2 , then the general solution is, y h ( x ) = c 1 e m 1 + c 2 e m 2 . Case 2: If the roots are real double roots m 1 and m 1 , then the general solution is, y h ( x ) = ( c 1 + c 2 x ) e m 1 . Case 3: If the roots are complex a ± i b , then the general solution is, y h ( x ) = e a x ( A cos ( b x ) + B sin ( b x ) ) . Calculation: Given that, the linear ordinary differential equation is ( D 2 + 4 π D + 4 π 2 I ) y = 0 . It can be written as y ″ + 4 π y ′ + 4 π 2 y = 0 . Compare the equation y ″ + 4 π y ′ + 4 π 2 y = 0 with the equation y ″ + a y ′ + b y = 0

10th Edition

ISBN: 9781119664697

Author: Kreyszig

Publisher: WILEY

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Chapter 2, Problem 12RQ

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The general solution of linear ordinary differential equation (D2+4πD+4π2I)y=0.

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Chapter 2, Problem 11RQ

Chapter 2, Problem 13RQ

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