Sive a solution to the system 2 y' - 25 - 8 æ(0)] -8 y solving the IVP with initial condition 30 -8 4 ¤(t) = exp( -1 vt)cos( 1 vt) exp( -1 vt) sin( 1 Vt) 30 -10 lote: Use the eigenvalue that makes the argument to the trig functions positve for t > 0. Part low take the derivative of the above solution and subtract – 1x(t) to obtain a second solution to the -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Give a solution to the system
25
-
x(0)
by solving the IVP with initial condition
y(0)
8
30
-8
4
*(t) =
exp( -1 vt)cos( 1 vt) +
exp( -1 vt) sin( 1
Vt)
-10
Note: Use the eigenvalue that makes the argument to the trig functions positve for t > 0.
Part 2 of 3
Now take the derivative of the above solution and subtract – 1x (t) to obtain a second solution to the
differential equation.
a'(t) + a(t) =
exp( – 1t)cos(1t) +
exp( – 1t)sin(1t)
30
Transcribed Image Text:Give a solution to the system 25 - x(0) by solving the IVP with initial condition y(0) 8 30 -8 4 *(t) = exp( -1 vt)cos( 1 vt) + exp( -1 vt) sin( 1 Vt) -10 Note: Use the eigenvalue that makes the argument to the trig functions positve for t > 0. Part 2 of 3 Now take the derivative of the above solution and subtract – 1x (t) to obtain a second solution to the differential equation. a'(t) + a(t) = exp( – 1t)cos(1t) + exp( – 1t)sin(1t) 30
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