Differential Equations of Order One

Separation of Variables

Given the differential equation
 

$M(x, y)\,dx + N(x, y)\,dy = 0$   ←   Equation (1)

 

where M and N may be functions of both x and y. If the above equation can be transformed into the form
 

$f(x)\,dx + f(y)\,dy = 0$   ←   Equation (2)

 

where f(x) is a function of x alone and f(y) is a function of y alone, equation (1) is called variables separable.