Definition:Separable Differential Equation/Also presented as

Separable Differential Equation: Also presented as

Some sources present this as an equation in the form:

$\dfrac {\d y} {\d x} = \dfrac {\map g x} {\map h y}$

or:

$\map h y \dfrac {\d y} {\d x} = \map g x$

whose general solution is found by solving the integration:

$\ds \int \map h y \rd y = \int \map g x \rd x + C$

Other sources have:

$\map g x + \map h y \dfrac {\d y} {\d x} = 0$

whose general solution is found by solving the integration:

$\ds \int \map g x \rd x = -\int \map h y \rd y + C$

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.7$: Homogeneous Equations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation: differential equations of the first order and first degree: $(2)$ Variables separable
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation: differential equations of the first order and first degree: $(2)$ Variables separable
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous): Appendix $8$: Common ordinary differential equations and solutions
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous): Appendix $9$: Common ordinary differential equations and solutions