One of the following is a general solution of the homogeneous differential equation y" – 7y + 10y = 0 ae" + be5a y = ae2* + be 5r ae2" + bebz y = ae" + be 5z and one of the following is a solution to the nonhomogeneous equation y" - 7y' + 10y = -8e" y = -6e" y = -2e" y = -8e" y = -4e" By superposition, the general solution of the equation y" – 7y' + 10y = -8e" is Find the solution with y(0) = 9 y(0)' = 4 y = 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 + 10y = 0 ae" + be5a y = ae2* + be 5r ae2" + bebz y = ae" + be 5z and one of the following is a solution to the nonhomogeneous equation y" - 7y' + 10y = -8e" y = -6e" y = -2e" y = -8e" y = -4e" By superposition, the general solution of the equation y" – 7y' + 10y = -8e" is Find the solution with y(0) = 9 y(0)' = 4 y = 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' + 10y = 0
y = ae" + besr
y = ge2r
+ be -5z
y = ae2* + be5z
y = aet + be 5z
and one of the following is a solution to the nonhomogeneous equation y"- 7y' + 10y = -8e"
y =
-6e"
y = -2e"
y = -8e"
y = -4e"
By superposition, the general solution of the equation y" 7y' + 10y = -8e" is
y =
Find the solution with
y(0) = 9
y(0)' = 4
y =
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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