Part 3: Solve the non- homogeneous equation y" + 49y = cos(7x) – 7æ² has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) -
Part 3: Solve the non- homogeneous equation y" + 49y = cos(7x) – 7æ² has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) -
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:Part 3: Solve the non-
homogeneous equation
y" + 49y = cos(7x) – 7x² 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) = -2
y(0)
= -5
Here is a graph of the solution to
the IVP
30
Transcribed Image Text:For the differential equation
y" + 49y = cos(7x) – 7x?
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-homogeneou
differential equation, we look for
functions annihilated by the
differential operator (a multiple of
the differential operator from
above)
s
Therefore the particular solution
must be made
up
of the functions
Substituting these into the
differential equation, we find the
particular solution is
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