Applications of Differential and Difference Equations(MAT2002)

Added on - 09 Nov 2020

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Experiment:4ASolution of homogeneous system of first orderand second order differential equations by matrixmethodQUESTION 1:Solve the system of differential equations y0 1 = 4y1 +y2 , y0 2 = 3y1 + 2y2, with the initial conditions y1(0)= 2, y2(0) = 0.AIM:finding solution of given differential equation with thehelp of given intial conditions givenMATLAB CODE:clcclearallcloseallsymst c1 c2A=input('Enter a square matrix :');[v,d]=eig(A)y1=c1*exp(d(1)*t)y2=c2*exp(d(4)*t)X=v*[y1;y2]IC=input('Enter ICs in theform[t0,x1(t0),x2(t0)] :');eq1=subs(X(1),IC(1))-IC(2);eq2=subs(X(2),IC(1))-IC(3);[c1,c2]=solve(eq1,eq2);X=subs(X)Department of Mathematics, School of advanced sciencesFall Semester2019-20Instructor: Dr. Aruna. KApplications of Differential and Difference Equations(MAT2002)
OUTPUT:X =(3*exp(5*t))/2 + exp(t)/2(3*exp(5*t))/2 - (3*exp(t))/2QUESTION 2 :Solve the system of differential equation y’’1 = 2y1+y2, y’’2 =y1+2y2, with the initial conditions y1(0) = 0,y’1(0) = 1, y2(0) =1,y’2(0) = 0.
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