# Solving by substitution

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## Solve by substitution

There are a lot of great apps out there to help students with their school work for Solving by substitution. Mathematical modeling is not necessarily very important to the exam (because most of the math exam focuses on solving), but in real life, especially in scientific research of science and engineering, mathematical modeling ability is a hard core ability. If a simpler and more accurate mathematical model can be established, it will almost be the final victory, and the rest of the solution will be left to the computer. People usually think that quick oral arithmetic and familiar formulas is a standard of strong mathematical ability. In fact, it is only the ability to solve problems (computational ability) in mathematical ability, and it can not be directly equivalent to mathematical ability itself.

Obviously, this equation is a univariate quadratic equation that we learned in junior high school, which is called the characteristic equation of differential equations here. So we transform a more complex second-order homogeneous linear differential equation with constant coefficients into a simpler one-dimensional quadratic equation, which has exactly two roots. One of the problems often encountered in mathematics is the solution of equations, especially in linear algebra. Today, we will use matlab to explore the solution of linear equations.

Reason: Lie groups and Lie algebras are one of the main axes of mathematics, capturing the concept of continuous symmetry. They are extended and generalized in various directions, such as infinite dimensional Lie algebras, Huck algebras, quantum groups or vertex operator algebras. Their structures and representations are usually related to each other in a deep way through D-modules or category equivalence. They are widely used in algebraic geometry, mathematical physics, harmonic analysis, number theory and other fields. The structural results of Lie groups are also extended to locally compact groups.

this analysis method is called time domain analysis method. If the time variable is transformed into other variables in order to solve the equation by hand, it is called transformation domain analysis method accordingly. This chapter mainly explains the time-domain analysis method, which is also the focus of the postgraduate entrance examination. When we are in contact with ordinary differential equations, we can only solve some special forms of equations, such as first-order linear differential equations, differential equations with separable variables, Bernoulli differential equations, etc.

The reason why we don't start with other equations is that these equations are easier to solve than other equations. The purpose of global differential equations is to solve dependent variables. The dependent variables in different time steps are solved by integrating time. The dependent variable can be used as the entry and exit of other fields. Such as speed or acceleration over time.

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this app can replace a scientific calculator pretty much and it’s the only app that can do so it can be a bit frustrating from time to time and the scanning feature does not work for long complex equations but the graphs are really good (even if it lacks the ability to add multiple equations) and the app has everything you could possibly need!

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