Separation of variables method

Separation of variables is a method used to solve certain types of differential equations. The method involves assuming that the solution to the differential equation can be expressed as a product of two functions, each of which depends on only one of the variables in the equation. For example, consider the partial differential equation: ∂u/∂t…

Solution of homogeneous differential equations of first order and first degree

A homogeneous differential equation of the first order and first degree is an equation of the form: dy/dx = f(x,y) where f(x,y) is a homogeneous function of degree 1 in x and y. In other words, if we replace y with ky and x with kx for any constant k, the function f(x,y) remains the…