1. Solve the following homogenous differential equations using two methods: 1) x(t) = et substitution and 2) Matrix eigenvalue method, 3) Using isoclines (a) 3x-4x=0; x(0) = 1 (0) = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solving second order differential equations
1. Solve the following homogenous differential equations using two methods: 1) x(t) = et substitution
and 2) Matrix eigenvalue method, 3) Using isoclines
(a) -3x-4x=0; x(0) = 1
(b) -5x+4x
=
0; x(0) 0
=
(0) = 0
(0) = 1
2. Solve the following homogenous differential equation -4x+5x=0 where x(0) = 1, (0) = 0.
3. Solve the following differential equation: +3 + 2x = t where x(0) = 1, (0) = 0. (For the particular
solution, use x(t) = At + B to substitute into the differential equation).
Transcribed Image Text:3 Solving second order differential equations 1. Solve the following homogenous differential equations using two methods: 1) x(t) = et substitution and 2) Matrix eigenvalue method, 3) Using isoclines (a) -3x-4x=0; x(0) = 1 (b) -5x+4x = 0; x(0) 0 = (0) = 0 (0) = 1 2. Solve the following homogenous differential equation -4x+5x=0 where x(0) = 1, (0) = 0. 3. Solve the following differential equation: +3 + 2x = t where x(0) = 1, (0) = 0. (For the particular solution, use x(t) = At + B to substitute into the differential equation).
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