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1. The differential equation +3 + 2x = 0 has the general solution x(1) = c1e+c2e-2 (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we can determine c, and cz by solving the equations x(0) = cje- + cz el-2)(0) = c¡(1) + c2(1) = 1, %3D x'(0) = c1(-1)e-0 + c>(-2)e~2x0) = -c1 – 2c2 = 1. (a) Find the values of c and c, by solving the above. (b) Find the solution of the differential equation subject to the specified initial condition by using the above method. i. y" – 3y - 4y = 0; y(0) = 0, y'(0) = 1. ii. y" – 9y' = 0; y(0) = 5, y'(0) = 0. %3D %3D %3D

1. The differential equation +3 + 2x = 0 has the general solution x(1) = c1e+c2e-2 (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we can determine c, and cz by solving the equations x(0) = cje- + cz el-2)(0) = c¡(1) + c2(1) = 1, %3D x'(0) = c1(-1)e-0 + c>(-2)e~2x0) = -c1 – 2c2 = 1. (a) Find the values of c and c, by solving the above. (b) Find the solution of the differential equation subject to the specified initial condition by using the above method. i. y" – 3y - 4y = 0; y(0) = 0, y'(0) = 1. ii. y" – 9y' = 0; y(0) = 5, y'(0) = 0. %3D %3D %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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1. The differential equation +34 + 2x = 0 has the general solution x(1) = c1e+c2e-2# (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we can determine c, and c2 by solving the equations x(0) = cje0 + c2e(-2)0) = c1(1) + c2(1) = 1, %3D x'(0) = c1(-1)e-0 + c>(-2)e~2x0) = -c1 – 2c2 = 1. (a) Find the values of c and c, by solving the above. (b) Find the solution of the differential equation subject to the specified initial condition by using the above method. i. y" – 3y – 4y = 0; y(0) = 0, y'(0) = 1. ii. y" – 9y' = 0; y(0) = 5, y'(0) = 0. %3D %3D
Transcribed Image Text:1. The differential equation +34 + 2x = 0 has the general solution x(1) = c1e+c2e-2# (by using the characteristic equation). If we are told that, when t = 0, x(0) = 1 and its derivative x'(0) = 1, we can determine c, and c2 by solving the equations x(0) = cje0 + c2e(-2)0) = c1(1) + c2(1) = 1, %3D x'(0) = c1(-1)e-0 + c>(-2)e~2x0) = -c1 – 2c2 = 1. (a) Find the values of c and c, by solving the above. (b) Find the solution of the differential equation subject to the specified initial condition by using the above method. i. y" – 3y – 4y = 0; y(0) = 0, y'(0) = 1. ii. y" – 9y' = 0; y(0) = 5, y'(0) = 0. %3D %3D
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