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For the differential equation y' + 8y + 16y = sin(7x)

For the differential equation y' + 8y + 16y = sin(7x)

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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For the differential equation y" + 8y + 16y = sin(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-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
Transcribed Image Text:For the differential equation y" + 8y + 16y = sin(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-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 3/" + 8y + 16y = sin(7x) has general solution (remember to use the format I gave you your your correct answer to the complementary functions above) Now that we have the general solution solve the IVP y(0) = 9 y(0) = 6
Transcribed Image Text:Part 3: Solve the non- homogeneous equation 3/" + 8y + 16y = sin(7x) has general solution (remember to use the format I gave you your your correct answer to the complementary functions above) Now that we have the general solution solve the IVP y(0) = 9 y(0) = 6
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