I’m trying to test a specific function as a solution to a nonlinear ODE in Maple. The equation is of the Riccati type, and my candidate solution involves parameters A, B, and C.
I've used assuming to specify the condition (4AC−B2)>0 and (4AC - B^2) <0, but when I use odetest to verify the solution, I still get a nonzero result. Additionally, when I apply the assumption, Maple sometimes introduces a negation sign in the output (e.g., changing sqrt(...) into -sqrt(...)), which wasn't part of the original solution.
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(1) |
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(2) |
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![S1 := G(xi) = (sqrt(4*A*C-B^2)*tan((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))-B)/(2*C)](/view.aspx?sf=240291_question/1dd90784b5cc7443de5e6e79b430d98d.gif)
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![G(xi) = (1/2)*((4*A*C-B^2)^(1/2)*tan((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))-B)/C](/view.aspx?sf=240291_question/633723ad479ce320aa292b39093f3cd1.gif)
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(3) |
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(4) |
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![S2 := G(xi) = -(sqrt(4*A*C-B^2)*cot((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)](/view.aspx?sf=240291_question/675423a39bc0d7f5abd67152058da24e.gif)
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![G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*cot((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C](/view.aspx?sf=240291_question/3c99356e0d90ae4442f70a846a032714.gif)
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(5) |
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(6) |
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![S3 := G(xi) = -(sqrt(4*A*C-B^2)*tanh((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)](/view.aspx?sf=240291_question/efc99669f4a7d371884d0d31c0715586.gif)
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![G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*tanh((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C](/view.aspx?sf=240291_question/10749bbec9b01130c326d0dccf0f15ad.gif)
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(7) |
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(8) |
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Download A2.mw
