How to Solve Differential Equations by Separation of Variables | General Solution

Опубликовано: 11 Октябрь 2024
на канале: John's Maths Book

In part 1 of this series, I explain how to use the separation of variables technique to solve first order differential equations and find the General Solution. I explain how to identify whether this technique can be used to solve a first order differential equation, specifically ensuring that the differential equation is a function of x, f(x), multiplied by a function of y, g(y). I emphasize that some algebraic manipulation may be required to get the equation into a form where the variables can be separated.

I then demonstrate how to separate the variables, x and y, by moving the y variables to the left hand side of the equation and the x variables to the right hand side of the equation and then integrating both sides of the equation to find the general solution to the differential equation.

I use two examples to demonstrate this technique in action to find the general solution of 1st order differential equations.