Classify equation certificate easily

Aug 6th, 2022
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How to classify equation certificate

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all right in this video were looking at the classification of differential equations theres three criteria here is a lot Nimet linear or non-linear first order second order we third fourth or any higher order up to n or is it ordinary or partial recommend spent too much time on this stuff really this video is just to introduce to you kind of the concept so you can you know just be able to classify differential equations and once you can do that then you can pick which methods which methods you need to solve them and well get more into the methods in another video but this is just kind of an introduction to the classification so first of all lets look at ordinary or partial so what Ive done here is actually Ive kind of color-coded these all into corresponding classifications and well get around to each of these by the end of the video but for ordinary or partial if a differential equation is ordinary it has ordinary derivatives in it only like regular derivatives like Y prime or

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A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system is inconsistent. If the slopes are different, the system is consistent and independent. If the slopes are the same and the y-intercepts are the same, the system is consistent and dependent.
A system of equations is consistent if it has at least one solution. A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions every point is a solution.
A system of equations is considered independent if the graphs of the equations create different lines. Independent systems of equations have one solution that can be found graphically or algebraically.
A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system is inconsistent. If the slopes are different, the system is consistent and independent. If the slopes are the same and the y-intercepts are the same, the system is consistent and dependent.
Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .
In the US, it has become common to introduce differential equations within the first year of calculus. Usually, there is also an Introduction to Ordinary Differential Equations course at the sophomore level that students take after a year of calculus.
A consistent independent system of equations will have one solution. A consistent dependent system of equations will have infinite number of solutions, and an inconsistent system of equations will have no solution.
Ordinary differential equations or (ODE) are equations where the derivatives are taken with respect to only one variable. That is, there is only one independent variable. Partial differential equations or (PDE) are equations that depend on partial derivatives of several variables.

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