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 cos 3 x + c 2 sin 3 x . The roots of the auxiliary equation are m 1 = 0 + 3 i and m 2 = 0 − 3 i . Denote both the roots variables as m . Therefore, the factors of the auxiliary equation are ( m − 3 i ) and ( m + 3 i ) . Multiply the factors and equate to zero. ( m − 3 i ) ( m + 3 i ) = 0 m 2 − 3 i m + 3 i m + 9 = 0 m 2 + 9 = 0 For an auxiliary equation y = e m x . Therefore, 1 = y e m x , m 2 = 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 53E

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To find: The homogeneous linear differential equation with constant coefficient whose general solution is y=c1cos3x+c2sin3x.

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Chapter 4.3, Problem 52E

Chapter 4.3, Problem 54E

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For each of the following series, determine whether the absolute convergence series test determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let Mi = 4, while if the test determines absolute convergence let Mi 1 : 2: ∞ Σ(−1)"+¹ sin(2n); n=1 Σ n=1 Σ ((−1)”. COS n² 3+2n4 3: (+ 4: 5 : n=1 ∞ n 2+5n3 ПП n² 2 5+2n3 пп n² Σ(+)+ n=1 ∞ n=1 COS 4 2 3+8n3 П ηπ n- (−1)+1 sin (+727) 5 + 2m³ 4 = 8. Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is -0.027 -0.621 -1.794 -1.132 -1.498 -4.355 -2.000 2.716

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

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Prob. 7E Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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

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To find: The homogeneous linear differential equation with constant coefficient whose general solution is y=c1cos3x+c2sin3x.

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