Definition:Exact Differential Equation/Definition 1

Definition

An exact differential equation is a first order ordinary differential equation in which the total differential is equal to zero:

$\dfrac {\partial f} {\partial x} \rd x + \dfrac {\partial f} {\partial y} \rd y = 0$

Also known as

An exact differential equation is often referred to just as an exact equation.

Also see

• Equivalence of Definitions of Exact Differential Equation

• Results about exact differential equations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation: differential equations of the first order and first degree: $(1)$ Exact equations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): exact equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation: differential equations of the first order and first degree: $(1)$ Exact equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): exact equation