# Changes

To find the solution of this equation, we assume that the solution is &phi; = constant. We assume that $\frac{\partial \phi}{\partial t} = M$ and $\frac{\partial \phi}{\partial y} = N$. (If we substitute M and N back into (1), it yields $(\frac{\partial \phi}{\partial t}) dt + (\frac{\partial \phi}{\partial y}) dy = 0$, which makes sense.)
To find $y/,$, manipulate the substitutions of M and N to get $M \partial t = \partial \phi$ and $N \partial y = \partial \phi$. Integrate both sides. To get the main function &phi; write the sum of each term found in each equation. For terms that appear in both equations, only write them once.
To find $y$, manipulate the substitutions of M and N to get $M \partial t = \partial \phi$ and $N \partial y = \partial \phi$. Integrate both sides. To get the main function &phi; write the sum of each term found in each equation. For terms that appear in both equations, only write them once.  To solve the expression for $y/,$, use the quadratic formula.