For the differential equation y" + 4y + 4y = x² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is List the complementary functions (the functions that make up the complementary solution) 8 . When you get this answer correct it will give you the format for the complementary solution that you must use below. 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 operator given above) Therefore the particular solution must be made up of the functions
For the differential equation y" + 4y + 4y = x² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is List the complementary functions (the functions that make up the complementary solution) 8 . When you get this answer correct it will give you the format for the complementary solution that you must use below. 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 operator given above) Therefore the particular solution must be made up of the functions
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:3:30
O O N a l73%
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
3y" + 4y/ + 4y = x² has general
solution (remember to use the
format I gave you in
answer to the complementary
functions above)
your correct
Now that we have the general
solution solve the IVP
y(0) = 6
y(0) = -2
Here is a graph of the solution to
the IVP
0.83518
II
Transcribed Image Text:3:29
自
令al 73%
For the differential equation
y' + 4y/ + 4y = x?
Part 1: Solve the homogeneous
equation
The differential operator for the
homogeneous equation is
List the complementary functions
the
(the functions that make
complementary solution)
. When
up
you
get this answer correct it will give
you the format for the
complementary solution that you
must use below.
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 operator given above)
Therefore the particular solution
must be made up of the functions
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