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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 di ff erential equation alone the general solution . For example, y ( t ) = ( b/a ) + C 1 e at would be the general solution for the di ff erential 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 . For 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 Di ff erential Equations. There are two: ODEs or ordinary di ff erential equations are di ff erential equations which do not involve partial deriva- tives. PDEs or partial di ff erential equations are di ff erential equations which do involve partial derivatives. Each of the examples of di ff erential 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. (For example, the rod might have
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