Exact differential equations belong to ODEs (Ordinary Differential Equations).
While you use partial derivatives to test for exactness and to find the potential function F(x,y), the equation itself describes a relationship between one independent variable (usually x) and one dependent variable
.
Key Summary
Classification: ODE.
Format: M(x, y)dx + N(x, y)dy = 0.
Why the confusion?: We use partial derivatives (\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}) as a tool to solve them, but the solution y(x) is a function of a single variable.
While you use partial derivatives to test for exactness and to find the potential function F(x,y), the equation itself describes a relationship between one independent variable (usually x) and one dependent variable
Key Summary
Classification: ODE.
Format: M(x, y)dx + N(x, y)dy = 0.
Why the confusion?: We use partial derivatives (\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}) as a tool to solve them, but the solution y(x) is a function of a single variable.