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(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 0.7 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 1 2 3 4 o 1 2 3 4 (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
f = @(t,x) [5*x(1);x(1)];

>> [t,y] = ode45...

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