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For the differential equation y"+25y = cos(5I)+ 1z² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D+25 List the complementary functions cos(5x), sin(5x) 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 1.xx, sin(5x) A Substituting these into the differential equation, we find the particular solution is sin(5x) + 10 21 625 25 Part 3: Solve the non-homogeneous equation y'+25y = cos(5z) + 1z has general solution (remember to use the format I gave you in your correct answer to the complementary functions 2 above) a cos(5x) +b sin(5x) 10 sin (5x)+ 25 625 Now that we have the general solution solve the IVP y(0) = 6 y (0) = 2

For the differential equation y"+25y = cos(5I)+ 1z² Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D+25 List the complementary functions cos(5x), sin(5x) 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 1.xx, sin(5x) A Substituting these into the differential equation, we find the particular solution is sin(5x) + 10 21 625 25 Part 3: Solve the non-homogeneous equation y'+25y = cos(5z) + 1z has general solution (remember to use the format I gave you in your correct answer to the complementary functions 2 above) a cos(5x) +b sin(5x) 10 sin (5x)+ 25 625 Now that we have the general solution solve the IVP y(0) = 6 y (0) = 2

Advanced Engineering Mathematics
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 give the correct functions annihilated by the differential operator and a list of functions the particular solution is made up of
For the differential equation y" + 25y = cos(5z) +lz? Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D2+ 25 List the complementary functions cos (5x), sin (5x) 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 1,x.r, sin(5x) A Substituting these into the differential equation, we find the particular solution is 10 sin (5x) + 25 625 Part 3: Solve the non-homogeneous equation y' +25y = cos(5x) + 1z² has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) a cos(5x) +b sin(5x) + sin (5x) + 2 10 25 625 Now that we have the general solution solve the IVP y(0) = 6 y (0) = 2 a 3:0 4/1
Transcribed Image Text:For the differential equation y" + 25y = cos(5z) +lz? Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D2+ 25 List the complementary functions cos (5x), sin (5x) 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 1,x.r, sin(5x) A Substituting these into the differential equation, we find the particular solution is 10 sin (5x) + 25 625 Part 3: Solve the non-homogeneous equation y' +25y = cos(5x) + 1z² has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) a cos(5x) +b sin(5x) + sin (5x) + 2 10 25 625 Now that we have the general solution solve the IVP y(0) = 6 y (0) = 2 a 3:0 4/1
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