Nonhomogeneous Linear ODEs

A system of n nonhomogeneous first order linear ODEs can be written in matrix forms as follows  

When b is a constant the vector equation (2.12) can be simplified by removing b from under the integral  

Equations (2.12) and (2.15) simplify to equation (2.7) (the homogeneous equations solution) when the forcing function b vector is the zero vector. The procedure for solving nonhomogeneous linear ODEs is presented next. 

Start Maple with a restart command to clear all variables. 

Call with(linalg) and with(plots) commands. 

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All the tanks are at an initial temperature of 20°C. Find the time it will take for the third tank to reach 99% of its steady state value. The values of the constants are W = 100 kg/min, M = 1000 kg, Cp = 2kJ/kg°C, and UA = 10kJ/min°C. Determine how this time varies with the parameters a and p. Equations (equation (2.17)) can be solved using Maple and the procedure described above for nonhomogeneous simultaneous linear ODEs follows. 

In fact, we also obtain precisely the same result from the z component of (12-38). So we see that (12 46) will satisfy the linearized equation of motion provided we choose U(r) to satisfy the nonhomogeneous ODE... 

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