## Second Order Differential Equation

Sub-Topics: Basics Of Second Order Differential Equation Coming soon!   Back To Mathematics For An Undergraduate Physics Course

## Basics Of Second Order Differential Equation

A second order differential equation is of the form $a \frac{d^{2}y}{dx^{2}} + b \frac{dy}{dx} + b \frac{dy}{dx} + cy = f(x)$. $f(x)$ is called a source term or forcing function. The differential equation is called a homogeneous equation IF $f(x) = 0$ non-homogeneous IF $f(x)$ is not 0. The steps involved in solving a homogeneous equation and non-homogeneous are quite …

## Variable Separable Differential Equation

A first order equation $\frac{dy}{dx} = f(x,y)$ is said to be variable separable if f(x,y) is of the form:$$g(x)h(y)$$ Steps to solve $\frac{dy}{dx} = g(x)h(y)$: Swap the variables around: $\frac{1}{h(y)}dy = g(x) dx$ Evaluate: $\int \frac{1}{h(y)} \, dy = \int g(x) \, dx$ You’re done! (Note: you might want to attempt to solve for y explicitly)   Back …

## Taylor Series

Taylor Series: Common Taylor Series: Back To Useful Mathematical References