with(LinearAlgebra): A:=Matrix([[2,1,1],[1,2,1],[1,1,2]]);#A:=Matrix([[-1,1,3],[-2,2,2],[-2,1,4]]); V:=Vector([s,s^2,s^3]);#V:=Vector([cos(s),sin(s),cos(s)]); X0:=Vector([1,2,3]); S1:=MatrixVectorMultiply(MatrixExponential(ScalarMultiply(A,t)),X0); B:=MatrixVectorMultiply(MatrixExponential(ScalarMultiply(A,t-s)),V): S2:=Vector([int(B[1],s=0..t),int(B[2],s=0..t),int(B[3],s=0..t)]); S:=VectorAdd(S1,S2);

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Y2w2Iy9JJCVpZEdGKEZhX2w=

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

A:=Matrix([[0,1,0],[0,0,1],[1,1,-1]]); V:=Vector([0,0,cos(t)]); X0:=Vector([1,0,0]); S1:=MatrixVectorMultiply(MatrixExponential(ScalarMultiply(A,t)),X0); B:=MatrixVectorMultiply(MatrixExponential(ScalarMultiply(A,t-s)),V): S2:=Vector([int(B[1],s=0..t),int(B[2],s=0..t),int(B[3],s=0..t)]); S:=VectorAdd(S1,S2); diff(S[2],t);

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systemeDiff:=proc(A,X) local i,n,L,D; n:=ColumnDimension(A); L:=Eigenvectors(A); D:=DiagonalMatrix(L[1]); for i to n do D[i,i]:=exp(D[i,i]*t) od; D,MatrixVectorMultiply(D,X); end: A:=Matrix([[-5,2,4,-4],[10,-3,-6,8],[11,-4,-6,8],[22,-8,-14,17]]); X:=Vector(<x,y,z,t>); systemeDiff(A,X);

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