Use matlab to answer this. Show me the coding Solution of ODES and Laplace Transforms 3. A

Use matlab to answer this. Show me the coding

 

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Solution of ODES and Laplace Transforms 3. A chemical mixer has the following mass and energy balances derived from first principles, that allow determining the exit concentration and temperature of a vessel: In which, dT dt dCa + Ca = Ca,in mass balance = Tim += (1/2) 0 Qenergy balance pvC = + T = Tin + | T2 dt Cain = 2 Ca(0) = 35 g L T1 T28 min = Tin = 35C T(0) = 90C cal Q=1.5 x 106. min p = 1000 L cal Cp=1- gxC v = 30 L/min Based on this information, please answer the following: a) Find the expressions that define the solutions of the concentration profile Ca(t) and the temperature profile T(t). You do not need to solve for a specific value in time, just to obtain the expressions. Use MATLAB and the symbolic toolbox. b) Find the Laplace transforms of the mass and energy balances. Similar to item (a), you do not need to solve the problem numerically, but instead find the expressions of Ca(s) and T(s). c) Based on the expressions obtained in item (b), find the inverse Laplace transforms of Ca(s) and T(s): That is, Ca(t) and T(t). Report if there are any differences from the results found in item (a). Again, use MATLAB. Solution of ODES and Laplace Transforms 3. A chemical mixer has the following mass and energy balances derived from first principles, that allow determining the exit concentration and temperature of a vessel: In which, dT dt dCa + Ca = Ca,in mass balance = Tim += (1/2) 0 Qenergy balance pvC = + T = Tin + | T2 dt Cain = 2 Ca(0) = 35 g L T1 T28 min = Tin = 35C T(0) = 90C cal Q=1.5 x 106. min p = 1000 L cal Cp=1- gxC v = 30 L/min Based on this information, please answer the following: a) Find the expressions that define the solutions of the concentration profile Ca(t) and the temperature profile T(t). You do not need to solve for a specific value in time, just to obtain the expressions. Use MATLAB and the symbolic toolbox. b) Find the Laplace transforms of the mass and energy balances. Similar to item (a), you do not need to solve the problem numerically, but instead find the expressions of Ca(s) and T(s). c) Based on the expressions obtained in item (b), find the inverse Laplace transforms of Ca(s) and T(s): That is, Ca(t) and T(t). Report if there are any differences from the results found in item (a). Again, use MATLAB.