Solving differential equations

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Homework Help Overview

The discussion revolves around solving a system of differential equations, specifically a pair of first-order equations with initial conditions. The original poster expresses uncertainty about whether the problem constitutes a system or two separate questions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss methods for solving first-order differential equations, with a focus on the Runge Kutta method as a numerical approach. There is also a question about the classification of the problem as a system of equations.

Discussion Status

The conversation is ongoing, with some participants providing guidance on the nature of the problem and suggesting methods for numerical solutions. There is an acknowledgment of the need to compare numerical results with exact solutions.

Contextual Notes

The original poster notes a requirement to use a specific numerical method (Runge Kutta) and expresses confusion regarding the classification of the problem. There is also a mention of posting in the correct forum for homework questions in the future.

johnchau123
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I have the following question. I am not sure if the question is a system of differential equations or it is actually 2 questions.

The question is as follows.
Solve the initial problems
x' = y, x(0)=0
y' = -x, y(0)=1
for 0 < t < 1 .

Thanks. :smile:
 
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Hi John and welcome to the forums,

For future reference please note that we have homework forums for such questions. However, in reply to your question, what methods do you know for solving first order differentials and which would be appropriate here?
 
Sorry for posting the questions in a wrong area, I will post my homework questions to an appropriate area next time. :smile:

Actually, the question requires us to use Runge Kutta method to solve the question, a numerical approach. However, I am confused if the question is a system of DE or it is actually questions.

Thanks. :smile:
 
Yes, it is a system of differential equations! It looks pretty close to trivial to solve directly. I expect that if you are being asked to solve it numerically you will also be expected to compare it to an exact solution.

The best way to handle a system of two equations with Runge Kutta is to set up two simultaneous "solvers", at each step using the values of x and y just calculated in the previous step to find the new values or x and y.
 

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