Linear differential equation

Okay kiddo, let me explain what a linear differential equation is.

First, let's start with what a differential equation is. A differential equation is an equation that involves a function and its derivatives. Do you remember what a derivative is? It's like finding the slope of a line, but for a curve or function.

Now, let's talk about what makes an equation linear. A linear equation is an equation that has a variable or function only to the first power (not squared or cubed or anything like that).

So, when we put these two things together, a linear differential equation is an equation that involves a function and its derivatives, but the function and its derivatives only appear to the first power (not squared, cubed, etc.).

For example, a simple linear differential equation could be something like:

dy/dx + 2y = 3x

This equation involves the function y and its derivative (the slope at any point on the curve) plus a constant (2y) that is multiplied by the function, and that must equal another constant (3x).

Solving a linear differential equation involves finding a function that satisfies the equation. This can be a bit tricky, but there are some common methods, like separation of variables, that can help.

So, in short, a linear differential equation is an equation that involves a function and its derivatives, but the function and its derivatives only appear to the first power. Solving these equations involves finding a function that satisfies the equation.