Bernoulli Differential Equations

A first order equation $\frac{dy}{dx} = f \left( x,y \right)$ is said to be a Bernoulli equation if f(x,y) is of the form $g \left( x \right) y + h \left( x \right) y^{a}$. Steps to solve $f \left( x,y \right) = g \left( x \right) y + h \left( x \right) y^{a}$: 1) Divide by ya to get $y^{-a} \frac{dy}{dx} …

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First Order Linear Differential Equation

$$\frac{dy}{dx} = p \left( x \right) y + q \left( x \right)$$ Procedure: – Calculate $I = \int p\left( x \right) \, dx$ – Find the integrating factors $e^{-I \left( x \right)}$ and $e^{I \left( x \right)}$ – Evaluate $\int e^{I \left( x \right)} q \left( x \right) \, dx$ – Hence the solution: $$y = e^{-I \left( x \right)} \left( …

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First Order Differential Equations

Sub-Topics: – Steps For Solving First Order Differential Equation – First Order Linear Differential Equation – Bernoulli Differential Equation – Variable Separable Differential Equation – Homogeneous Differential Equation – Exact Differential Equation – Non-Exact Differential Equation Back To Mathematics For An Undergraduate Physics Course

Mathematics For An Undergraduate Physics Course

This post is meant to identify and briefly teach you the mathematics needed for a Physics course. (Not all) I will provide links to the websites that teach the relevant topics. Year 1 Calculus Integration without integration Differential Equations First Order Differential Equations Second Order Differential Equations Linear Algebra Coordinate Transformation Under Rotation Great lecture series by MIT (Youtube): httpvp:// ____________________________________ …

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Integration Table

Table Of Basic Integrals Basic Forms \begin{equation} \int x^n dx = \frac{1}{n+1}x^{n+1},\hspace{1ex}n\neq -1 \end{equation} \begin{equation} \int \frac{1}{x}dx = \ln |x| \end{equation} \begin{equation} \int u dv = uv – \int v du \end{equation} \begin{equation} \int \frac{1}{ax+b}dx = \frac{1}{a} \ln |ax + b| \end{equation} Integrals of Rational Functions \begin{equation} \int \frac{1}{(x+a)^2}dx = -\frac{1}{x+a} \end{equation} \begin{equation} \int (x+a)^n dx = \frac{(x+a)^{n+1}}{n+1}, n\ne -1 …

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