ODE Test Fails for Solution

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Question:ODE Test Fails for Solution

Posted: salim-barzani 1785 Product: Maple 2024

May 01 2025

I’m trying to verify a solution given in the form from using Maple's odeTest. Even though the paper claims the solution satisfies the ODE, Maple does not simplify the result to zero. Could someone explain why the test fails or suggest the correct way to verify it in Maple?

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Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`. See ?protect for details.

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(cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))*(-A)^(1/2)+(B*sin(2*(-A)^(1/2)*(xi+xi[0]))+A+B)^(1/2)*(-cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))

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G(xi) = 1/(B^(1/2)*(xi+xi[0]))

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-csgn(1/(xi+xi[0]))/(B^(1/2)*(xi+xi[0])^2)-1/(B^(1/2)*(xi+xi[0])^2)

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G(xi) = 1/((-B)^(1/2)*(xi+xi[0]))

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-(-1/(xi+xi[0])^2)^(1/2)*xi[0]/((-B)^(1/2)*(xi+xi[0])^2)-(-1/(xi+xi[0])^2)^(1/2)*xi/((-B)^(1/2)*(xi+xi[0])^2)-1/((-B)^(1/2)*(xi+xi[0])^2)

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(sgn(A)*(A*B)^(1/2)*(tan((A*B)^(1/2)*xi[0])^2+1)*(tan((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((tan((A*B)^(1/2)*xi)+tan((A*B)^(1/2)*xi[0]))^2*sgn(A)^2+(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2))/(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2

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(sgn(A)*(A*B)^(1/2)*(cot((A*B)^(1/2)*xi[0])^2+1)*(cot((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((cot((A*B)^(1/2)*xi[0])*cot((A*B)^(1/2)*xi)-1)^2*sgn(A)^2+(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2))/(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2

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(A*(sgn(A)^2-1)*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))-sgn(A)^2*A+2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A)/(1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

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(sgn(A)^2*A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+sgn(A)^2*A-2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+A)/(-1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))