Module for the Differential Operator Method for Systems of D. E.

Numerical Methods for O. D. E. using Mathematica. (c) John H. Mathews, 2003

Differential Operator Method for a D. E. System.

    Solution of a homogeneous first order linear system of differential equations.

      
      

The differential operator is used to write the system in the form

      
      

Then eliminate y[t] and obtain

      

Solve this second order linear differential for x[t]. To obtain the second solution y[t] use the first equation in the system to get y[t].

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Exercise 1(a)  Find the general solution to the system of D. E.'s  
          

Exercise 1(b)  Find the solution with the initial conditions:
          

Exercise 2 (a)  Find the general solution to the system of D. E.'s  
        

Exercise 2(b)  Find the solution with the initial conditions:
          

Exercise 3(a)  Find the general solution to the system of D. E.'s  
          

Exercise 3(b)  Find the solution with the initial conditions: