Variable separable( differential equations)with defination and example

 

What is variable separable

The equation M (x)dx+N(y)dy=0 can be solved by variable separable 

M(x) function depending on x

M(y) function depending on y

Operator (dy,dx) should be in numenator

For example:

                       dy/dx =x/y

                    ydy = xdx

Integrating 

                    ∫ydy=∫xdx

                   y^2/2+c= x^2/2+c

                    y^2/2-x^2/2≠c'

                    y^2-x^2=c'