Changes

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

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

To find the solution of this equation, we assume that the solution is &phi; = constant. We can re-write a different form of this equation by substituting <math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>. This yields <math>(\frac{\partial \phi}{\partial t}) dt + (\frac{\partial \phi}{\partial y}) dy = 0</math>, which makes sense.

To find the solution of this equation, we assume that the solution is &phi; = constant. We can re-write a different form of this equation by substituting <math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>. This yields <math>(\frac{\partial \phi}{\partial t}) dt + (\frac{\partial \phi}{\partial y}) dy = 0</math>.

to find &phi;, we integrate M with respect to t and N with respect to y. This will give us two different equations. To find &phi; , we  

To find &phi;, we integrate M with respect to t and N with respect to y. This will give us two different equations. To find &phi; , we  

Go through the example to find &phi; by integrating, then check that

Go through the example to find &phi; by integrating, then check that