# Solving a system of differential equations by elimination

• I
• polibuda
In summary, the conversation revolved around the topic of solving system differential equations by elimination. The person in question wanted to know if their approach was correct and asked for someone to check their sample task. They also mentioned finding a movie demonstrating the method, but were unsure if it was accurate. They had sent it to their instructor, who was unfamiliar with the method and advised them to prove its correctness before using it. The conversation also included a request for the problem statement and a suggestion to verify the solution for x(t) and y(t) themselves. Overall, the conversation highlighted concerns about the accuracy and validity of the method used for solving system differential equations by elimination.
polibuda
TL;DR Summary
Checking solution
I would to know if I'm solving system differential equation by elimination correctly. Could somebody check my sample task and tell if something is wrong?

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Well, I don't see any problem in my thread. I want to ask if this method is correct. I found a movie with way how to solve system differential equtions by elimination, but I can't verify it is ok. The film:

I sent it to my instructor and he said he don't know this method, and when I want to use from it I need to prove, that the method is correct.

polibuda said:
Well, I don't see any problem in my thread.
Neither do I. The least you can do is type out the problem statement for this thread

polibuda said:
Could somebody check my sample task and tell if something is wrong?
You can check your work yourself by verifying that what you found for x(t) and y(t) satisfy the original differential equations.

As @BvU already hinted at, this should have been posted in one of the Homework sections. Also, squeezing 2 1/2 pages of work into a single image makes your work difficult to read.

## 1. What is a system of differential equations?

A system of differential equations is a set of equations that describes the relationship between a set of variables and their rates of change. These equations are used to model dynamic systems in various fields such as physics, engineering, and biology.

## 2. What is elimination method for solving a system of differential equations?

The elimination method involves using algebraic operations to eliminate one variable from a system of equations, leaving a simpler equation with fewer variables. This method is commonly used to solve linear systems of equations.

## 3. When is elimination method the best approach for solving a system of differential equations?

The elimination method is best suited for systems of differential equations that are linear and have a small number of variables. It may not be the most efficient method for solving nonlinear systems or systems with a large number of variables.

## 4. What are the steps involved in solving a system of differential equations by elimination?

The steps for solving a system of differential equations by elimination are as follows:1. Write the equations in standard form.2. Choose a variable to eliminate.3. Use algebraic operations to eliminate the chosen variable.4. Solve the resulting equation for the remaining variable.5. Substitute the value of the remaining variable into one of the original equations to find the value of the eliminated variable.6. Repeat the process until all variables have been eliminated.7. Check the solution by substituting the values into the original equations.

## 5. Are there any limitations to using the elimination method for solving a system of differential equations?

Yes, the elimination method may not work for systems of differential equations that have singular matrices or inconsistent equations. In these cases, other methods such as substitution or matrix methods may be more suitable.

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