Explanation Procedure used: Find a homogenous equation with the constant coefficients whose general solution is provided. 1 Determine the roots of the auxiliary equation from the solution given and obtain the auxiliary equation. 2 Determine the homogenous linear equation from the auxiliary equation. Calculation: Consider the given general solutions y = c 1 e − 4 x + c 2 e − 3 x . The roots of the auxiliary equation are m 1 = − 4 and m 2 = − 3 . Denote both the roots variables as m . Therefore, the factors of the auxiliary equation are ( m + 4 ) and ( m + 3 ) . Multiply the factors and equate to zero. ( m + 4 ) ( m + 3 ) = 0 m 2 + 4 m + 3 m + 12 = 0 m 2 + 7 m + 12 = 0 For an auxiliary equation y = e m x . Therefore, 1 = y e m x , m 2 = y ″ e m x and m = y ′ e m x

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter 4.3, Problem 50E

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To find: The homogeneous linear differential equation with constant coefficient whose general solution is y=c1e−4x+c2e−3x.

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Chapter 4.3, Problem 49E

Chapter 4.3, Problem 51E

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Differential Equations with Boundary-Value Problems (MindTap Course List)

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The homogeneous linear differential equation with constant coefficient whose general solution is y = c 1 e − 4 x + c 2 e − 3 x .

Solution Summary: The author explains the procedure used to find a homogeneous linear differential equation with constant coefficients whose general solution is provided.

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To find: The homogeneous linear differential equation with constant coefficient whose general solution is y=c1e−4x+c2e−3x.

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