To determine To explain: The definition of an exact ODE and determine whether the ODE f ( x ) d x + g ( y ) d y = 0 is exact. Explanation An equation which contains one or more derivatives of an unknown function is called an ordinary differential equation. An ODE is called exact M ( x , y ) d x + N ( x , y ) d y = 0 when there exists a function u ( x , y ) of two variables whose continuous partial derivatives ∂ M ∂ y = ∂ N ∂ x are equal. The given ODE is f ( x ) d x + g ( y ) d y = 0

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Chapter 1, Problem 5RQ

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To explain: The definition of an exact ODE and determine whether the ODE f(x)dx+g(y)dy=0 is exact.

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