MA 36600 LECTURE NOTES: FRIDAY, JANUARY 163If we did not keep track of the initial conditiony(0) =y0, we would call the solution of the differentialequation alone thegeneral solution. For example,y(t) = (b/a) +C1eatwould be the general solution for thedifferential equation above because it involves an arbitrary constantC1. If we do keep track of the initialcondition, we would call the solution theparticular solution. For example,y(t) = (b/a)+(y0−b/a)eatwouldbe the particular solution corresponding toy(0) =y0.Classification of Differential EquationsTypes of Differential Equations.There are two:•ODEsorordinary differential equationsare differential equations which do not involve partial deriva-tives.•PDEsorpartial differential equationsare differential equations which do involve partial derivatives.Each of the examples of differential equation we have seen are types of ODEs, so here is an example of aPDE: Say that we have a rod of lengthLsitting in or above a heat source. (For example, the rod might have
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