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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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)
Expert Solution
Step 1: To find.
In this question, we will find the solution of the differential equations.
Step by step
Solved in 5 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
