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I would like to know how to solve the following differential equation (you may refer to this post for the original question):
Thank you very much.
In this short how-to, I will show how to solve 2nd-order differential equation of the form:
y''(t) = f(y)
I will give an example at the end.
In this how-to, I am going to solve a recurrence differential equation using Binomial Expansion Theorem for non-commutative elements.
This equation is an inhomogeneous version of the equation in this post.
How to solve this equation:
This tutorial provides several example in solving linear non-homogeneous ordinary differential equation(NVODE) using operator factorization method.
In general there are no guaranteed methods to solve non-homogeneous ordinary differential equation with variable coefficients(NVODE) analytically. In this paper, I am going to use operator method to solve NVODE of order n.
The method is about factorizing the differential operator. In order to do so, we first need to know one of the fundamental solutions of the order n ...
This question is inspired by this post.
In the above post, it asked about how to solve the following equation:
At the first sight, I think I would like to try using the following form as a particular solution: ...
This how-to provides an example to Solving system of first order linear differential equations with matrix exponential method.
I will teach the general theory of how to solve first order linear differential equations in this tutorial.
In this tutorial, I will first introduce what differential equation is. Separable first order differential equation will be solved. Then the integrating factor will be taught to solve linear differential equation of the first degree. The auxiliary equation (or characteristic equation) will be introduced to solve homogeneous linear equations, and then operator method will be taught finally to solve non-homogeneous linear equations. ...
