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olve the following initial value problem and 1. y" + y' + 9.25y = 0, y(0) = 2 %3D

olve the following initial value problem and 1. y" + y' + 9.25y = 0, y(0) = 2 %3D

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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Solve the following initial value problem and present its particular solution: 1. y" + y' + 9.25y = 0, y(0) = 2, y'(0) = 8 2. y" + y' – 2y = 0, y(0) = -4, y'(0) = -5 %3D 3. y" + y' + 0.25y = 0, y(0) = 3, y'(0) = -3.5 %3D %3D
Transcribed Image Text:Solve the following initial value problem and present its particular solution: 1. y" + y' + 9.25y = 0, y(0) = 2, y'(0) = 8 2. y" + y' – 2y = 0, y(0) = -4, y'(0) = -5 %3D 3. y" + y' + 0.25y = 0, y(0) = 3, y'(0) = -3.5 %3D %3D
(2²+a2 + b) = 0 The solution to the ODE depends on the nature of the roots of the characteristic equation EULER IDENTITIES ea+ib o FOR DIS TRcseR FUS d=4=2 SHARE. = e"(cos b + i sin b) %3D 1 cos y =(e'y + e-iy) sin y = (ety – e-ly) Two Distinct Real Roots 1 Real Double Root 2i 1 y = cze21*+ c2xe?2* 5(e +e-Y) cosh y = 2 1 Complex Conjugate Roots 11 = a + ib 12 = a – ib sinh y =(ey – e-") ey = cosh y + i sinh y e-y = cosh y - i sinh y y = eax(C1 cos bx + c2 sin bx)
Transcribed Image Text:(2²+a2 + b) = 0 The solution to the ODE depends on the nature of the roots of the characteristic equation EULER IDENTITIES ea+ib o FOR DIS TRcseR FUS d=4=2 SHARE. = e"(cos b + i sin b) %3D 1 cos y =(e'y + e-iy) sin y = (ety – e-ly) Two Distinct Real Roots 1 Real Double Root 2i 1 y = cze21*+ c2xe?2* 5(e +e-Y) cosh y = 2 1 Complex Conjugate Roots 11 = a + ib 12 = a – ib sinh y =(ey – e-") ey = cosh y + i sinh y e-y = cosh y - i sinh y y = eax(C1 cos bx + c2 sin bx)
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