JSFHrestart:Load the needed packageswith(LinearAlgebra):with(linalg):Read the text-file containing the implementationread "/Users/elbacha/Desktop/Maple/Programmation_text/Internet/Frobenius_MDE.txt";Enter the matrices of your higher order linear diferential system (they must be of type "Matrix")A2:=Matrix(2,2,[x^2-1,x,0,x^2-1]);A1:=Matrix(2,2,[0,0,0,0]);A0:=Matrix(2,2,[5*x^2+1,x,1,x^3]);Run the algorithm for computing a basis of the regular solution space of A2*theta^2(Y) + A1*theta(Y) + A0*Y = 0,
where theta=x*d/dx. The series involved are computed up to order 5.Sol:=Frobenius_MDE([A2,A1,A0],x,{},5);VerificationChoose a solution, i.e., an element of the list Sol[1]Y:=Sol[1,1];
Verification that A2*theta^2(Y)+A0*Y=0 mod x^6Verification([A2,A1,A0],Y,x);Choose a solution, i.e., an element of the list Sol[1]Y:=Sol[1,3];
Verification that A2*theta^2(Y)+A0*Y=0 mod x^5Verification([A2,A1,A0],Y,x);JSFHTTdSMApJN1JUQUJMRV9TQVZFLzQzMjEwMTA1OTJYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMlIiMiIywmKiQlInhHIiIjIiIiISIiRisiIiFGKUYnRiY=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TTdSMApJN1JUQUJMRV9TQVZFLzQ1Mzk2MDY5NTJYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMqJiUieEciIiIsLiIiKUYpRigjIiM7IiIkKiRGKCIiIyMiI1QiIicqJEYoRi4jIiVUPCIkMCUqJEYoIiIlIyInPDh1Iic/YjoqJEYoIiImIyIqVF0ieUAiKSsrL29GKSomRihGKSwuRitGKUYoI0Y5Ri5GLyMiIyopIiNhRjQjIiVUciIlIVsnRjgjIihkYkQkIigrISkpUUY9IyIrVElrSDoiKysrV1xDRilGJg==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TTdSMApJN1JUQUJMRV9TQVZFLzQ1Mzk2MTI0NzJYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJComJSJ4RyIiJywqISs2VUwyTiIiIkYpIStEWSteTC0lI2xuRzYjRikiKzUvOnlAKiZGL0YtRilGLSIrXShRKnpGRi0jRi0iKSshM0EnLCQqJkYpRiosLiErK0slSHgiRi1GKSEqRENBJVsqJEYpIiIjISkoXHNyI0YvIiorZ2hcKEYzIipdX3RjKSomRilGPUYvRi0iKXFiYktGLSNGLSIqK2dUQyJGJg==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