Seshu cheera

Here are some important points about differential equations: Definition of a Differential Equation : A differential equation is an equation that involves the derivative (or derivatives) of a dependent variable with respect to an independent variable (or variables). These equations are fundamental in various fields, including Physics, Chemistry, Biology, Anthropology, Geology, and Economics, highlighting their prime importance in modern scientific investigations . For example, the equation dy/dx = g(x) , where y = f(x) , is a differential equation. Similarly, dy/dx + x/y = 0 is a differential equation because it involves variables and the derivative of y with respect to x . Types of Differential Equations : Ordinary Differential Equation : This type involves derivatives of the dependent variable with respect to only one independent variable . The sources primarily focus on ordinary differential equations. An example is d²y/dx² + (dy/dx)² = 0 . Partial Differential Equati...