An equation that involves an independent, variable, dependent variable and differential coefficients of dependent variable with respect to the independent variable is called a DIFFERENTIAL EQUATION. For example: 

1. \(\cfrac{{dy}}{{dx}} = \cos x\)
2. \(\cfrac{{dy}}{{dx}} + y\sin x = \cos x\)
3. \({x^2}{\left( {\cfrac{{{d^2}y}}{{d{x^2}}}} \right)^2} + {x^3}{\left( {\cfrac{{dy}}{{dx}}} \right)^3} = 7{x^2}{y^2}\)
4. \(\cfrac{{{d^2}y}}{{d{x^2}}} + {\left[ {1 + {{\left( {\cfrac{{dy}}{{dx}}} \right)}^2}} \right]^{3/2}} = 0\)
5. \(y=1+x \left( {\cfrac{{dy}}{{dx}}} \right) + \cfrac{{{x^2}}}{{2!}}{\left( {\cfrac{{dy}}{{dx}}} \right)^2} + \cfrac{{{x^3}}}{3}{\left( {\cfrac{{dy}}{{dx}}} \right)^3} + ........\cfrac{{{x^n}}}{{n!}}{\left( {\cfrac{{dy}}{{dx}}} \right)^n} + ......\infty \)