A differential equation of the first order and first degree can be expressed in any one of the following forms: 

\[\frac{{dy}}{{dx}} = f(x,y);\]\[\frac{{dy}}{{dx}} = \frac{{f(x,y)}}{{g(x,y)}};\]\[f\left( {x,y} \right)dx + g\left( {x,{\rm{ }}y} \right)dy = 0\]

Integrating the above equation, we get the solution of the differential equation that must contain arbitrary constant. Note that all the differential equations are not integrable. A very limited standard forms of differential equations can only be solved, some of which are given below:

• Variables separable from
• Differential equation reducible to variables separable form: 
• Homogenous differential equations: 
• Differential equations reducible to homogenous equations:
• Linear differential equation: 
• Differential equation reducible to linear form (Bernoulli’s equation)