Changes

<math>M(t,y) + N(t,y)y' = 0\,</math>

<math>M(t,y) + N(t,y)y' = 0\,</math>

or

or

<math>M(t,y) dt + N(t,y) dy = 0\,</math>

<math>M(t,y) dt + N(t,y) dy = 0\,</math>

To find the solution of this equation, we assume that the solution is &phi; = constant.

To find the solution of this equation, we assume that the solution is &phi; = constant. This means that:

This means that <math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>

<math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>

 

&phi; is found by integrating M and N:

&phi; is found by integrating M and N:

:<math>\phi(t, y) = \int_0^t M(s, 0) ds + \int_0^y N(t, s) ds</math>

:<math>\phi(t, y) = \int_0^t M(s, 0) ds + \int_0^y N(t, s) ds</math>