theorem of existence and uniqueness for first order linear differential ...
Nov 9, 2013 · This doesn't mean that there isn't a unique solution to the differential equation, just that the existence-uniqueness theorem for first-order linear differential equations won't provide the answer.
Understanding the General Solution of First-Order Linear Differential ...
Jan 28, 2025 · Why is the general solution to ordinary first-order differential equations the sum of a homogeneous solution (obtained by setting the inhomogeneous term to 0) and a particular solution …
General solution of nonlinear first order differential equation
May 9, 2020 · The reason why the arbitrary constant vanishes is because it represents a singular solution of the differential equation. The singular solution is basically like an envelope of all the …
How to express a 2nd order ODE as 1st order ODE's?
as a system of 1st order ODEs and verify there exists a global solution by invoking the global existence and uniqueness theorems. I'm not sure how to express second order ODEs as first order ODEs, any …
Solving nonlinear first order differential equations
Feb 8, 2014 · Solving nonlinear first order differential equations Ask Question Asked 11 years, 10 months ago Modified 11 years, 10 months ago
ordinary differential equations - Practical applications of first order ...
Dec 22, 2014 · In elementary ODE textbooks, an early chapter is usually dedicated to first order equations. It is very common to see individual sections dedicated to separable equations, exact …
First-order system differential equation initial conditions
Oct 9, 2024 · I am studying systems controls and in exploring first order systems I got confused on how to properly model a system with initial conditions. This is the differential equation for a first order wit...
ordinary differential equations - Why are they called "first integrals ...
Apr 26, 2019 · (See " Ordinary Differential Equations " by Vladimir I. Arnol'd) If you integrate the given differential equation for the first time you got the first integral . If you again integrate the first integral …
trigonometry - Trigonometric First Order Differential Equation ...
Mar 6, 2018 · See this link http://mathworld.wolfram.com/ExactFirst-OrderOrdinaryDifferentialEquation.html for information on exact equations of the First Order. Or get …
Linear vs nonlinear differential equation - Mathematics Stack Exchange
Jun 8, 2013 · How to distinguish linear differential equations from nonlinear ones? I know, that e.g.: $$ y''-2y = \\ln(x) $$ is linear, but $$ 3+ yy'= x - y $$ is nonlinear. Why?