**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.