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1. Find y(t) for the following ODE. dt2d2y+6dtdy+8y=2y(0)=y(0)=0 2. Example 4.8 Solution of the CST Thermal Mixer Equation ( 3rd edition textbook) Example 4.8 Solution of the CST Thermal Mixer Equation Problem Statement. The dynamic equation for a CST themal 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. Deternine the time behavior of T, assuming that at time equal to zero, T is equal to T2 and a step thange in T, of magnitude A is implemented at time equal to zero while all other inputs remuin cosstant. 3. Example 4.10 Solution of Second-Order Differential Equations ( 3nd edition textbook) Example 4.10 Solution of Second-Order Differential Equations Problem Statement. Consider a general scoond-onder differential equation dt2d2y+adidy+by=r(t)(drdy)t=0=0y(0)=0 and fn is a step change from 0 to 1 at t=0. Evalate the solutions for this differential equation. Noec that because this is a second-order differential equation, two initial conditions are required to solve it. Thres cases can rewh for this yyaten