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One of the following is a general solution of the homogeneous differential equation y" + 5y + 6y = 0 y = ae 3³ + be-22 y = ae-3 + bez y=ae² + be-2z y = ae²+ be2 and one of the following is a solution to the nonhomogeneous equation y" + 5y +6y=36e* y = 3e² y = 9e² y = 6e² y = 12e² By superposition, the general solution of the equation y" + 5y' + 6y = 36e² is y = Find the solution with y = y(0) = 3 3/ (0) = 5 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be The fundamental theorem tells me that that this is the unique solution to the IVP on the interval (-00.00)

One of the following is a general solution of the homogeneous differential equation y" + 5y + 6y = 0 y = ae 3³ + be-22 y = ae-3 + bez y=ae² + be-2z y = ae²+ be2 and one of the following is a solution to the nonhomogeneous equation y" + 5y +6y=36e* y = 3e² y = 9e² y = 6e² y = 12e² By superposition, the general solution of the equation y" + 5y' + 6y = 36e² is y = Find the solution with y = y(0) = 3 3/ (0) = 5 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be The fundamental theorem tells me that that this is the unique solution to the IVP on the interval (-00.00)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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One of the following is a general solution of the homogeneous differential equation y" + 5y +6y=0 y = ae + be-2 y = ae-3x + b₂ 2x be2x By superposition, the general solution of the equation y" + 5y' +6y=36e* is y = Find the solution with -3x and one of the following is a solution to the nonhomogeneous equation y" + 5y + 6y = 36e* y = 3e* y=9c² y = 6e* y = 12e² y = y = ae* + be-22 y = ae" + be 2 y(0) = 3 y'(0) = 5 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be . The fundamental theorem tells me that that this is the unique solution to the IVP on the interval (-∞0,00)
Transcribed Image Text:One of the following is a general solution of the homogeneous differential equation y" + 5y +6y=0 y = ae + be-2 y = ae-3x + b₂ 2x be2x By superposition, the general solution of the equation y" + 5y' +6y=36e* is y = Find the solution with -3x and one of the following is a solution to the nonhomogeneous equation y" + 5y + 6y = 36e* y = 3e* y=9c² y = 6e* y = 12e² y = y = ae* + be-22 y = ae" + be 2 y(0) = 3 y'(0) = 5 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be . The fundamental theorem tells me that that this is the unique solution to the IVP on the interval (-∞0,00)
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