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Solve a system of differential equations by using StateSpaceModel?

Posted 1 year ago
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Hi guys,

I have tried to solve a system of differential equations by using StateSpaceModel and StateResponse. The system has four parts, so I put four state space models. My approach for solve it was use StateResponse for Part I considering symbolic initial conditions. Then, I used StateResponse to solve Part II considering the initial conditions as the solution of the Part I. The same for Part III, in which the initial conditions are the solutions of Part II; and the same for Part IV. Each part is a system of 7 differential equations and symbolic coefficients (A1,A2,A3,A4,Ar,Af,QL). In addition, the independent variable wt is replaced by other terms, such as wt1, Dc and wt2. In general, the system is dependent of symbolic terms: A1,A2,A3,A4,Ar,Af,QL,wt1,Dc and wt2. I have attached the code. The problem is that when I try to solve Part IV, mathematica is running forever... I have waited for 12 hours and nothing. Someone has an idea about what is happening? Should I still waiting until mathematica find a solution? Or, maybe it is impossible to solve Part IV considering the complexity of this part?

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