Definition:Separable Differential Equation/General Form

Definition

A first order ordinary differential equation which can be expressed in the form:

$\map {g_1} x \map {h_1} y + \map {g_2} x \map {h_2} y \dfrac {\d y} {\d x} = 0$

is known as a separable differential equation.

Its general solution is found by solving the integration:

$\ds \int \frac {\map {g_1} x} {\map {g_2} x} \rd x + \int \frac {\map {h_2} y} {\map {h_1} y} \rd y = C$

Also see

• Solution to Separable Differential Equation

• Results about separable differential equations can be found here.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 18$: Basic Differential Equations and Solutions: $18.1$: Separation of variables
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 19$: Basic Differential Equations and Solutions: $19.1.$: Separation of variables