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18.03ESG Notes 1 Pramod N. Achar

Summary: 18.03­ESG Notes 1
Pramod N. Achar
Fall 1999
Yesterday in class, the question arose of how one might derive the integrating
factor to use in solving a first-order linear equation:
+ P(x)y = Q(x). (1)
We want to multiply through by some (x) such that the left-hand side becomes
recognizable as the derivative of something. (The right-hand side stays just a
function of x, so we can just integrate it.)
+ P(x)(x)y = Q(x)(x) (2)
More specifically, we are going to try to obtain the left-hand side as the result
of using the product rule for differentiation. Looking at the two terms on the
left-hand side, we see that one contains dy/dx and the other contains y, so it is
reasonable to suppose that y ought to be one of the factors in the product we're
looking for. Moreover, everything else on the left-hand side is just a function of


Source: Achar, Pramod - Department of Mathematics, Louisiana State University


Collections: Mathematics