| Line 3: | Line 3: | ||
=== <small> 4.0 Abstract <small> === | === <small> 4.0 Abstract <small> === | ||
| − | <font size="3px"> In last tutorial we looked at three basic methods to solve differential equations in the first order. In a linear equation, we can switch the variable <math>x</math> to a higher order, like <math>x^2</math>, <math>x^3</math>, ..., <math>x^n</math> to obtain higher-ordered equations. Similarly, the differential term <math>\frac{dy}{dx}</math> can also be switched as <math>\frac{d^2y}{dx^2}</math>, <math>\frac{d^3y}{dx^3}</math>, ..., <math>\frac{d^ny}{dx^n}</math>. This gives us the basic idea of differential equations in higher orders, the most general form for which is like <math>f_n(t)\frac{d^ | + | <font size="3px"> In last tutorial we looked at three basic methods to solve differential equations in the first order. In a linear equation, we can switch the variable <math>x</math> to a higher order, like <math>x^2</math>, <math>x^3</math>, ..., <math>x^n</math> to obtain higher-ordered equations. Similarly, the differential term <math>\frac{dy}{dx}</math> can also be switched as <math>\frac{d^2y}{dx^2}</math>, <math>\frac{d^3y}{dx^3}</math>, ..., <math>\frac{d^ny}{dx^n}</math>. This gives us the basic idea of differential equations in higher orders, the most general form for which is like <math>f_n(t)\frac{d^ny}{dt^n}+f_{n-1}\frac{d^{n-1}y}{dt^{n-1}}+...+f_1(t)\frac{dy}{dt}+f_0(t)y=g(t)</math>, where <math>n</math> is the order. |
The </font> | The </font> | ||
Revision as of 01:44, 17 November 2017
Introduction to ODEs in Higher Orders
A slecture by Yijia Wen
4.0 Abstract
In last tutorial we looked at three basic methods to solve differential equations in the first order. In a linear equation, we can switch the variable $ x $ to a higher order, like $ x^2 $, $ x^3 $, ..., $ x^n $ to obtain higher-ordered equations. Similarly, the differential term $ \frac{dy}{dx} $ can also be switched as $ \frac{d^2y}{dx^2} $, $ \frac{d^3y}{dx^3} $, ..., $ \frac{d^ny}{dx^n} $. This gives us the basic idea of differential equations in higher orders, the most general form for which is like $ f_n(t)\frac{d^ny}{dt^n}+f_{n-1}\frac{d^{n-1}y}{dt^{n-1}}+...+f_1(t)\frac{dy}{dt}+f_0(t)y=g(t) $, where $ n $ is the order.
The
