# Ordinary D.F equations, their order and degree

Differential equation: An equation containing an independent variable, dependent variable and differential coefficient of dependent variable with respect to independent variable is called a differential equation. Order of a differential equation: The order of a differential Equation is the order of the highest order derivative appearing in the equation.

For example, in the equation $$\frac{{{d}^{2}}y}{d{{x}^{2}}}+3\frac{dy}{dx}+2y={{e}^{x}}$$, the order of highest order derivative is 2. So. It is a differential equation of order 2.

The equation $$\frac{{{d}^{2}}y}{d{{x}^{2}}}-6{{\left( \frac{dy}{dx} \right)}^{2}}-4y=0$$ is of the order 2, It is a differential equation of order 2.

Degree of a differential equation: The degree of a differential equation is the degree of the highest order derivative, when differential coefficient are made free from radicals and fractions.

Example I: Consider the differential equation $$\frac{{{d}^{2}}y}{d{{x}^{2}}}-6{{\left( \frac{dy}{dx} \right)}^{2}}-4y=0$$.

In this equation the number of highest order derivative is 2. So it is a differential equation of degree 1.

Example II: Consider the differential equation $$x{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2}}+{{\left( \frac{dy}{dx} \right)}^{4}}+{{y}^{2}}=0$$.

In this equation, the order of the highest order derivative is 3. And its power is 2. So it is a differential equation of order 3 and degree 2.