Question
Transcribed Text
(a) Solve y" - 5y =0,y(0) = 1,y(0) = 2 analytically; (b) solve the
same problem with Matlab, for 0<15 3; (c) plot both the exact solutions obtained
in (a) and the numerical solution in (b) with different colors.
Consider the system
dx1 = X1 - X2
dt
dx2 dt = X1 + X2
with X1 =
(a) Solve the system and write down the exact solution.
1
1
0.9
0.8
0.8
0.6
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0.4
0.6
0.2
0.5
0.4
-0.2
0.3
-0.4
0.2
-0.6
0.1
-0.8
-1
o
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o
1
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(b) Use Matlab to solve the system.
(c) Plot on the same figure the exact solution and the numerical solution of X1 (t),
obtained in (a) and (b) respectively.
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q.1 (a)>>dsolve('D2y = 5*Dy', 'y(0) = 1', 'Dy(0) = 2')
ans =
(2*exp(5*t))/5 + 3/5
1(b)
>>
f = @(t,x) [5*x(1);x(1)];
>> [t,y] = ode45...
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