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To find <math>y</math>, manipulate the substitutions of M and N to get <math>M \partial t = \partial \phi</math> and <math>N \partial y = \partial \phi</math>. 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.
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To find <math>y</math>, manipulate the substitutions of M and N to get <math>M \partial t = \partial \phi</math> and <math>N \partial y = \partial \phi</math>. Integrate both sides. This will give us <math>\phi(t)\,</math> and <math>\phi(y)\,</math>. To get <math>\phi(t, y)\,</math>, write the sum of each term found in each equation. For terms that appear in both equations, only write them once.
     

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