# Solution of a simple Differential Equation

## Main Question or Discussion Point

Hi,

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

d2x/dt2= k*dy/dt

Sorry
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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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.

Edited.

Hootenanny
Staff Emeritus
Gold Member
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.

I just got the solution on paper. You're too fast Hootenanny...

Cheers guys, I think i understand (think i was being a bit dumb) getting confised about my boundary conditions.