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Example 4.8 Solution of the CST Thermal Mixer Equation Problem Statement. The dynamic equation for a CST thermal mixing tank is given by Equation 3.5.7, i.e., MdtdT=F1T1+F2T2(F1+F2)T where T is the dependent variable of the process and F1,F2,T1 and T2 are inputs to the process. Determine the time behavior of T, assuming that at time equal to zero, T is equal to T0 and a step change in T1 of magnitude A is implemented at time equal to zero while all other inputs remain constant. 3. Example 4.10 Solution of Second-Order Differential Equations ( 3rd edition textbook) Example 4.10 Solution of Second-Order Differential Equations Problem Statement. Consider a general second-order differential equation dt2d2y+adtdy+by=f(t)(dtdy)t=0=0y(0)=0 and f(t) is a step change from 0 to I at t=0. Evaluate the solutions for this differential equation. Note that because this is a second-order differential equation, two initial conditions are required to solve it. Three cases can result for this system: Case 1a24b>0 Case 2a24b=0 Case 3a24b