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2 4 Exact Equations Class Notes

# 2 4 Exact Equations Class Notes - Differential Equations...

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1 Differential Equations Section 2.4 Exact Equations Recall from Calculus III o If then the differential is given by . o If is a constant so that then we have . Suppose we have the equation . What is ? Note that we have a differential equation with solution . The differential equation given above is called an exact differential equation. o In general, the differential equation is an exact differential equation if and only if there exists some function such that and . o Criterion for an Exact Differential Equation Let M and N be continuous and have continuous first partial derivatives in a rectangular region in the plane, then the equation above is exact if and only if . Determine if the following equations are exact. o o Now the question becomes, if we know a differential equation is exact, then how do we find the function such that is a solution to the differential equation?

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2 Steps to solve an exact differential equation 1) Put the equation in standard form and check to make sure it2. is exact.
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