For the differential equation y"+4y cos(2z)+9z² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D2+4 List the complementary functions cos (2x), sin(2x) 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" + 4y = cos(2x) + 9x2 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) = -4 / (0) = -6
For the differential equation y"+4y cos(2z)+9z² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D2+4 List the complementary functions cos (2x), sin(2x) 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" + 4y = cos(2x) + 9x2 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) = -4 / (0) = -6
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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Please answer all parts of the question correctly
Transcribed Image Text:For the differential equation y"+4y cos(2z)+9z²
Part 1: Solve the homogeneous equation
The differential operator for the homogeneous equation is D2+4
List the complementary functions cos (2x), sin(2x)
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)
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" + 4y = cos(2x) + 9x2 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) = -4
y (0) = -6
9:49 PM
4/16/2021
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