1. Math 3120 Differential Equations with Boundary Value Problems Chapter 4: Higher-Order Differential Equations Section 4-9: Solving Systems of Linear Differential Equations by Elimination

2. Solving Systems of Linear DE by Elimination Many physical problems involve a number of separate elements linked together in some manner. For example, electrical networks, predator-prey model, mixture problems, etc. In the above cases, the corresponding mathematical problems consists of a system of two or more DE. These systems of DE contain derivatives of two or more dependent variables, each of which is a function of the same independent variable. A solution of a system of DE is a set of sufficiently differentiable functions that satisfies each equation in the system on some common interval.

3. Method of Solution All terms involving the dependent variable to are brought to one side and group the same variables. Write each equation in the system of differential operator notation. Eliminate one of the variables. Eliminate all variables in the given systems.

4. Example: Solve

5. Example: Solve

6. Example: Solve