Solution of a simple Differential Equation

In summary, the conversation is about a person seeking help with solving a differential equation involving two dependent variables, x and y, and a constant k. They mention needing the solution to find the position of a particle in a magnetic field. Another person suggests differentiating the first equation and substituting it into the second to obtain a third order homogeneous ODE in y, which can be solved easily. The original person thanks them for their help.
  • #1
gabrown
8
0
Hi,

I was wondering if anyone could help me solve or even know the type of the differential equation below

d2x/dt2= k*dy/dtSorry
I also have

d2y/dt2= -k*dx/dt

where k is a constant.

I need it to find the position x when looking at a particle going through a magnetic field.

Thanks very much

Gareth
 
Last edited:
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  • #2
Are you sure about the equation? It has two dependent variables, x and y as functions of t. Because you only have one equation this seems strange.
 
  • #3
Edited.
 
  • #4
In that case I would suggest differentiating the first ODE with respect to t and then substituting it into the second. Upon substitution, you will obtain a third order homogenous ODE in y which can be solved trivially.
 
  • #5
I just got the solution on paper. You're too fast Hootenanny...
 
  • #6
Cheers guys, I think i understand (think i was being a bit dumb) getting confised about my boundary conditions.
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many physical, chemical, and biological processes in science and engineering.

2. What is a simple differential equation?

A simple differential equation is a type of differential equation that involves only one independent variable and its derivatives. It can be solved using basic calculus techniques, such as integration and differentiation.

3. How do you solve a simple differential equation?

To solve a simple differential equation, you need to find the general solution, which is a family of solutions that satisfies the equation. This can be done by separating variables, using the method of undetermined coefficients, or using the variation of parameters method.

4. Why are differential equations important in science?

Differential equations are important in science because they allow us to model and understand complex systems and phenomena. They are used in many fields, including physics, chemistry, biology, and engineering, to make predictions and solve real-world problems.

5. What are some applications of simple differential equations?

Simple differential equations have many applications in science, such as modeling the growth of a population, the decay of a radioactive substance, the motion of a pendulum, and the flow of fluids. They are also used in economics, finance, and other social sciences to model and analyze various systems.

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