# The Applications of Ordinary Differential Equation (Term Paper Sample)

no specific instruction from professor

just a paper that solve a problem use ode. For example use ode to predict the population or predict a simple economic model or anything use ode to solve

For the linear systems of ordinary differential equations, we will have to consider the effects of some unknown functions on one another. The two by two system of ordinary differential equations will look something like this:

Let’s say that Y has been set to an unknown vector and A has been set as coefficient matrix, then we will have the following matrix equation

Second Theorem: Let’s suppose that the values of coefficient matrix A are in the form of λ = α ± iβ, then the solution will be as following:

It should be noted that both the imaginary and real parts will acts as independent solutions to the ordinary differential equation system.

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