For the differential equation y" +16y +64y= sin(6z) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is List the complementary functions 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) Therefore the particular solution must be made up of the functions Substituting these into the differential equation, we find the particular solution is Part 3: Solve the non-homogeneous equation y' + 16y + 64y= sin(6x) has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) Now that we have the general solution solve the IVP y(0) = -3 y(0) = -8

For the differential equation y" +16y +64y= sin(6z) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is List the complementary functions 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) Therefore the particular solution must be made up of the functions Substituting these into the differential equation, we find the particular solution is Part 3: Solve the non-homogeneous equation y' + 16y + 64y= sin(6x) has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) Now that we have the general solution solve the IVP y(0) = -3 y(0) = -8

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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Question

Please answer all parts and give correct answers

For the differential equation y" +16f + 64y= sin(6z)
Part 1: Solve the homogeneous equation
The differential operator for the homogeneous equation is
List the complementary functions
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)
Therefore the particular solution must be made up of the functions
Substituting these into the differential equation, we find the particular solution is
Part 3: Solve the
on-homogeneous equation
y' + 16y + 64y= sin(6x) has general solution (remember to use the format I gave you in your correct answer to the complementary functions
above)
Now that we have the general solution solve the IVP
y(0) = -3
/(0) = -8
1:08
A O G qx /13
(?
a
Cup
立

Now that we have the general solution solve the IVP
y(0) = -3
(0)
=-8
Here is a graph of the solution to the IVP
30
<-30

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