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lecture_3 (dragged) 2 - MA 36600 LECTURE NOTES FRIDAY...

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MA 36600 LECTURE NOTES: FRIDAY, JANUARY 16 3 If we did not keep track of the initial condition y (0) = y 0 , we would call the solution of the diFerential equation alone the general solution . ±or example, y ( t )=( b/a )+ C 1 e at would be the general solution for the diFerential equation above because it involves an arbitrary constant C 1 . If we do keep track of the initial condition, we would call the solution the particular solution . ±or example, y ( t b/a )+( y 0 b/a ) e at would be the particular solution corresponding to y (0) = y 0 . Classification of Differential Equations Types of DiFerential Equations. There are two: ODEs or ordinary diferential equations are diFerential equations which do not involve partial deriva- tives. PDEs or partial diferential equations are 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 a PDE: Say that we have a rod of length L sitting in or above a heat source. (±or example, the rod might have
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