MATH 1005 Lecture Notes - Lecture 9: Integrating Factor
18 Jan 2015
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Document Summary
If we try to solve non-exact equations using our potential function method, we will hit a snag (when solving for c(x) or c(y), these will not be single variable functions, they will be multivariable functions. This means that we must find an integrating factor i(x,y) that when multiplied by our initial ordinary differential equation we will have our new p(x,y) and q(x,y) satisfy the exact property. In general: this is a tough thing to do! So we will be working on two different types of easier integrating factors to try. If they fail, we will not try to do any other integrating factors. Consider the ode as , and consider an integrating factor i(x,y) that will make this exact. If we use the product rule we get: As we can see this is already turning messy. However, assume that our integrating factor is only a function of x, this means that iy = 0 and would give us:
