Step 1:

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Definition of an Exact first order differential equation :

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The equation \"\" is an exact differential equation if there exists a function f of two variables x and y having continuous partial derivatives such that \"\".
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The general solution of the equation is \"\", where C is a constant.
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\"\".
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The function \"\" should be there, since in our integration, we assumed that the variable y is constant.
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Step 2:
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The differential equation is \"\".

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Compare the above equation with \"\".

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\"\"

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\"\"

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Find \"\".

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Consider \"\".

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Apply partial derivative on each side with respect to y.

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\"\"

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Consider \"\".

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Apply partial derivative on each side with respect to x.

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.\"\"

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Since \"\" it is an exact differential equation.

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The solution of \"\" is \"\".

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\"\"
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,
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\"\"
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\"\".
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\"\"

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Now find \"\".

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\"\"

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Substitute \"\" in equation (1).

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\"\".

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Thus the solution is \"\", where C  is a constant.

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\"\", where C is a constant.
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The solution of the differential equation is \"\", where C is a constant.

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