Given that the characteristic equation has the following roots , what is the complementary solution? 1+ 3i, 1± 3i, 2, 2, 2, 2, 4 O a y = e²[(a – bz)cos3iz + (c + dz)sin3iz] + (e + fz + gx² + hæ³)e2z + tez O b. y = e*[(a + bz)cos3z – (c+ dz)isin3z] + (e + fx + gz² + hæ³)e²z + te# Ocy = e*[(a + bæ)cos3z + (c + dz)sin3z] + (e + fz + gz² + hæ*)e²= + te“ O d. y = e"[(a + bz)cos3z + (c + dz)isin3r] + (z + gz² + hæ³)e²= + tetz
Given that the characteristic equation has the following roots , what is the complementary solution? 1+ 3i, 1± 3i, 2, 2, 2, 2, 4 O a y = e²[(a – bz)cos3iz + (c + dz)sin3iz] + (e + fz + gx² + hæ³)e2z + tez O b. y = e*[(a + bz)cos3z – (c+ dz)isin3z] + (e + fx + gz² + hæ³)e²z + te# Ocy = e*[(a + bæ)cos3z + (c + dz)sin3z] + (e + fz + gz² + hæ*)e²= + te“ O d. y = e"[(a + bz)cos3z + (c + dz)isin3r] + (z + gz² + hæ³)e²= + tetz
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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![Given that the characteristic equation has the following roots, what is the complementary solution?
1+ 3i, 1+ 3i, 2, 2, 2, 2, 4
O a. y = e=[(a – bæ)cos3ix + (c+ dæ)sin3ix] + (e + fx + gx² + hæ³)ez + te4z
O b. y = e²[(a + bæ)cos3z – (c+ dz)isin3x] + (e + fx + gz² + hz³)e²z + te*z
Ocy = e"[(a + bæ)cos3z + (c + dz)sin3z| + (e + fx + ga² + hæ*)e²= + te
O d. y = e"[(a + bæ)cos3z + (c + dæ)isin3r] + (x + gæ² + hæ³)e²= + tetz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef138319-bc76-4a69-9875-20daf6575ed7%2Fc86195f7-638a-4f7d-91f0-5a66e5889ae5%2F6ub0de_processed.png&w=3840&q=75)
Transcribed Image Text:Given that the characteristic equation has the following roots, what is the complementary solution?
1+ 3i, 1+ 3i, 2, 2, 2, 2, 4
O a. y = e=[(a – bæ)cos3ix + (c+ dæ)sin3ix] + (e + fx + gx² + hæ³)ez + te4z
O b. y = e²[(a + bæ)cos3z – (c+ dz)isin3x] + (e + fx + gz² + hz³)e²z + te*z
Ocy = e"[(a + bæ)cos3z + (c + dz)sin3z| + (e + fx + ga² + hæ*)e²= + te
O d. y = e"[(a + bæ)cos3z + (c + dæ)isin3r] + (x + gæ² + hæ³)e²= + tetz
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