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Linear, First-Order Difference Equations. In this chapter we will learn how to solve autonomous and non-autonomous linear, fi-. Separation of variables is a technique commonly used to solve first order ordinary differential equations. It is so-called because we rearrange the equation We now present two applied problems modeled by a first-order linear differential equation. RL Circuits. The diagram in Figure 16.5 represents an electrical Since there is only one arbitrary constant , taking the first difference A general linear difference equation of order ' ' with constant coefficients is be able to apply solutions of first-order difference equations to contextual problems. 14.0 Introduction. Imagine you are to jump from an aircraft at an Assume we have a first order differential equation of the form dy dt. = f (t,y) with intial conditions y(t0) = y0. Alan H. SteinUniversity of Connecticut.