One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0 -3z ae + be 42 y = ae? + be ae 3z + be1z y = ae? + be 4z and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e y = -8e y = -2e y = -4e 6e By superposition, the general solution of the equation y" + 7y + 12y = -40e is Find the solution with y(0) = 2 y' (0) = 7 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
One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0 -3z ae + be 42 y = ae? + be ae 3z + be1z y = ae? + be 4z and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e y = -8e y = -2e y = -4e 6e By superposition, the general solution of the equation y" + 7y + 12y = -40e is Find the solution with y(0) = 2 y' (0) = 7 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
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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Transcribed Image Text:One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0
3z
ae
+ be 4z
y = ae" + be 1
ae 3z + be1z
y = ae? + be 4z
and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e
y = -8e
y = -2e
y = -4e
6e
By superposition, the general solution of the equation y" + 7y' + 12y = -40e is
Find the solution with
y(0) = 2
y' (0) = 7
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
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