Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Blair Zhang on November 20, 2018, 03:15:56 PM

Title: integrating factor
Post by: Blair Zhang on November 20, 2018, 03:15:56 PM
How to derive the integrating factor for function only depends on x?
Title: Re: integrating factor
Post by: wuyuning on November 20, 2018, 03:22:19 PM
Here is one way to prove it.

We need to find a factor so that make the ODE become exact.
So μ(x, y)M(x, y) + μ(x, y)N(x, y)y = 0, if the equation is exact, then (μM)y = (μN)x.
Further more, Mμy − Nμx + (My − Nx)μ = 0. You are asking about integrating factor only depends on x, so it is safe to assume that μy = 0(taking derivative with respect to y).  then we find that dμ/dx= μ(My − Nx)/N. If (My − Nx)/N is a function of x only, then there is an integrating factor μ that also depends only on x.

I hope this brief explanation helps. :)

Title: Re: integrating factor
Post by: Victor Ivrii on November 20, 2018, 04:48:13 PM
Search and read before you write
http://forum.math.toronto.edu/index.php?topic=1242.0 (http://forum.math.toronto.edu/index.php?topic=1242.0)