Solving differential equations

In summary, The question asks to solve a system of two differential equations using the Runge Kutta method for 0 < t < 1. The methods of solving first order differentials will be appropriate in this case. The poster is confused if the question is a system of DE or actually two separate questions and it is clarified that it is a system of DE. The best way to solve this system using Runge Kutta is to set up two simultaneous "solvers" at each step.
  • #1
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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  • #2
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?
  • #3
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:
  • #4
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.

What is a differential equation?

A differential equation is an equation that relates one or more functions with their derivatives. It expresses the relationship between the rate of change of a variable and the variable itself.

Why are differential equations important?

Differential equations are important because they are used to model and understand various natural phenomena and physical systems. They are also essential in engineering and other branches of science for predicting and analyzing the behavior of systems.

What are the different methods for solving differential equations?

There are various methods for solving differential equations, such as separation of variables, substitution, and integration. Other methods include using power series, Laplace transforms, and numerical methods.

What are initial value problems and boundary value problems?

Initial value problems involve finding a solution to a differential equation that satisfies given initial conditions, while boundary value problems involve finding a solution that satisfies given conditions at specific points or intervals.

What are some real-world applications of solving differential equations?

Differential equations have a wide range of applications in many fields, including physics, chemistry, biology, economics, and engineering. They are used to model various phenomena such as population growth, heat transfer, and electrical circuits, among others.

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