# Solving differential equations

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. ## Answers and Replies

Hootenanny
Staff Emeritus
Science Advisor
Gold Member
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. 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. HallsofIvy
Science Advisor
Homework Helper
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.