### Ordinary Differential Equations

Ordinary Differential Equations

A differential equation is an equation with $\frac{d^n}{dx^n}$ terms. Let's start with a simple equation with two variables $x$ and $y$.

$y = ae^x + be^{3x}$

If we differentiate this in $x$, a first order differential equation comes as

$\frac{dy}{dx} = ae^x + 3be^{3x}$

If we differentiate it once more in terms of $x$, a second order differential equation is produced as

$\frac{d^2y}{dx^2} = ae^x + 9be^{3x}$

By solving there three equations, we can get an equation without those constant terms $a$ and $b$ and that is called an ordinary differential equation.

A differential equation is an equation with $\frac{d^n}{dx^n}$ terms. Let's start with a simple equation with two variables $x$ and $y$.

$y = ae^x + be^{3x}$

If we differentiate this in $x$, a first order differential equation comes as

$\frac{dy}{dx} = ae^x + 3be^{3x}$

If we differentiate it once more in terms of $x$, a second order differential equation is produced as

$\frac{d^2y}{dx^2} = ae^x + 9be^{3x}$

By solving there three equations, we can get an equation without those constant terms $a$ and $b$ and that is called an ordinary differential equation.