Differential Equations
1.0 Introduction
1.0 Introduction
An equation involving independent variables, dependent variables and the derivatives of the dependent variables is called a differential equation.
It is an equation in $x$ and $y$ and derivatives of $y$ with respect to $x$ i.e., $y$ is a dependent variable on $x$ and the equation involving $x$, $y$ and derivatives of $y$ with respect to $x$ is a differential equation. $$\frac{{dy}}{{dx}} = x{e^x}$$$${\left( {\frac{{dy}}{{dx}}} \right)^2} = px + q$$
There are two types of differential equation:
(i) Ordinary differential equation: If the dependent variables depend only on one independent variable $x$, then the differential equation is called
the ordinary differential equation. For example: $$\frac{{dy}}{{dx}} + xy = \sin x$$
(ii) Partial differential equation: If the dependent variables depend on two or more independent variables, then the differential equation is called the
partial differential equation. For example: $$\frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0$$
