For the differential equation y"-0y – 16y= e 4z Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is 16 List the complementary functions -4x se A Part 2: Find the particular solution To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differenti: operator from above) e cos (8x) 4x Therefore the particular solution must be made up of the functions 1,-x A Substituting these into the differential equation, we find the particular solution is -4x xe Part 3: Solve the non-homogeneous equation y' - Oy - 16y = e 4z has general solution (remember to use the format I gave you in your correct answer to the complementary functions abov -4x 4x ae + be 4x_ xe

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Please give correct answers for each box
For the differential equation y"- Oy-16y e
Part 1: Solve the homogeneous equation
The differential operator for the homogeneous equation is D-16
List the complementary functions4x
4x
A
Part 2: Find the particular solution
To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differential
operator from above)4x
cos (8x)
Therefore the particular solution must be made up of the functions 1, -x
Substituting these into the differential equation, we find the particular solution is
-4x
xe
8
Part 3: Solve the non-homogeneous equation
y' – Oy – 16y = e-4z has general solution (remember to use the format I gave you in your correct answer to the complementary functions above)
-4x
ae
4x
+be 4r
xe
8.
Now that we have the general solution solve the IVP
y(0) = -9
y (0) = -9
梦
a
3:07 PM
4/15/20
Transcribed Image Text:For the differential equation y"- Oy-16y e Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D-16 List the complementary functions4x 4x A Part 2: Find the particular solution To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differential operator from above)4x cos (8x) Therefore the particular solution must be made up of the functions 1, -x Substituting these into the differential equation, we find the particular solution is -4x xe 8 Part 3: Solve the non-homogeneous equation y' – Oy – 16y = e-4z has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) -4x ae 4x +be 4r xe 8. Now that we have the general solution solve the IVP y(0) = -9 y (0) = -9 梦 a 3:07 PM 4/15/20
The differential operator for the homogeneous equation is D-16
List the complementary functions
4x
Part 2: Find the particular solution
To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differential
operator from above)
cos ( 8x)
Therefore the particular solution must be made up of the functions 1,-x
Substituting these into the differential equation, we find the particular solution is
4x
xe
Part 3: Solve the non-homogeneous equation
y' - Oy - 16y =e 4z has general solution (remember to use the format I gave you in your correct answer to the complementary functions above)
-4x
xe
aex
+ be 4x
8
Now that we have the general solution solve the IVP
y(0) = -9
y (0) = -9
-4x
217 Ax - 359e
-4x xe
8
64
梦 $
3:08 I
4/15/2
Transcribed Image Text:The differential operator for the homogeneous equation is D-16 List the complementary functions 4x Part 2: Find the particular solution To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differential operator from above) cos ( 8x) Therefore the particular solution must be made up of the functions 1,-x Substituting these into the differential equation, we find the particular solution is 4x xe Part 3: Solve the non-homogeneous equation y' - Oy - 16y =e 4z has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) -4x xe aex + be 4x 8 Now that we have the general solution solve the IVP y(0) = -9 y (0) = -9 -4x 217 Ax - 359e -4x xe 8 64 梦 $ 3:08 I 4/15/2
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Basics of Inferential Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,