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 diFerentialequation alone thegeneral solution. ±or example,y(t)=(b/a)+C1eatwould be the general solution for thediFerential equation above because it involves an arbitrary constantC1. If we do keep track of the initialcondition, we would call the solution theparticular solution. ±or example,y(tb/a)+(y0−b/a)eatwouldbe the particular solution corresponding toy(0) =y0.Classification of Differential EquationsTypes of DiFerential Equations.There are two:•ODEsorordinary diferential equationsare diFerential equations which do not involve partial deriva-tives.•PDEsorpartial diferential equationsare diFerential equations which do involve partial derivatives.Each of the examples of diFerential 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. (±or example, the rod might have
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