For the differential equation y" + 2y +ly = sin(7x) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is (D+1)- List the complementary functions re 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 sin ( 7x), cos(7r) Substituting these into the differential equation, we find the particular solution is Part 3: Solve the non-homogeneous equation y' + 2y + ly = sin(7x) 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) = -9

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please answer all parts of the question correctly
For the differential equation y" +2y +1y= sin(7z)
Part 1: Solve the homogeneous equation
The differential operator for the homogeneous equation is (D+1)-
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 sin (7x), cos( 7x)
Substituting these into the differential equation, we find the particular solution is
Part 3: Solve the non-homogeneous equation
y' + 2y + ly = sin(7x) 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) = -9
y (0) = 5
a
9:50 PM
A A O 4x
4/16/2021
Transcribed Image Text:For the differential equation y" +2y +1y= sin(7z) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is (D+1)- 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 sin (7x), cos( 7x) Substituting these into the differential equation, we find the particular solution is Part 3: Solve the non-homogeneous equation y' + 2y + ly = sin(7x) 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) = -9 y (0) = 5 a 9:50 PM A A O 4x 4/16/2021
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