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riccati_system can find a closed-form solution for certain systems of riccati ODEs. A system of riccati ODEs of n variables is:
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where are the unknown functions and are polynomials in of second degree with function coefficients.
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To solve this system, riccati_system tries to convert it into a matrix equation,
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where , and are n by n matrices. The user can request this matrix form instead of a full solution by using the 'matrix_only' option. In this case a sequence is returned.
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This function is part of the DEtools package, and so it can be used in the form riccati_system(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[riccati_system](..).
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