Ordinary or partial differential equation

1. Mar 5, 2015

MarkZone

1. The problem statement, all variables and given/known data
x(d^2y/dx^2)+dx/dt+xy=0
2. Relevant equations

3. The attempt at a solution
At first I thought it was an ODE, but then I found out the derivative was respect to to variables x and t.
I am not sure if it is an ODE or PDE. What are the dependent and independent variables in the equation? Is it linear?

Last edited: Mar 5, 2015
2. Mar 6, 2015

Simon Bridge

Written like this: $$x\frac{d^2}{dx^2}y + \frac{d}{dt}x + xy = 0$$... then we can conclude that y is a function of x and x is a function of t. i.e. $y(t)=y\big(x(t)\big)$ is the solution.
This happens a lot in physics where you happen to know dx/dt by some other means.

If it were a partial DE then you'd expect to see dy/dx and dy/dt - telling up that y is a function of both x and t separately and we can write y as y(x,t).

Where did you find this equation, in what context?

Last edited: Mar 6, 2015
3. Mar 7, 2015

MarkZone

Sorry for late response. The differential equation is the stress analysis of aerodynamics. I wonder if it is a partial or ordinary differential equation.

4. Mar 7, 2015

Simon Bridge

If y is a function of both x and t, separately, then it is partial - otherwise it isn't.
What physical quantities do x y and t represent?

5. Mar 7, 2015

MarkZone

I really don't know. It is a math problem without any further context.

6. Mar 7, 2015

Simon Bridge

You just said it was to do with stress analysis in an airframe. Does airframe stress not have any physical quantities to measure that have relationships to each other?

Whatever - without any further context, the answer is the same as post #2 ... it is an ordinary DE where y is a function of x and x is a function of t. You could reconstruct the whole thing in terms of t by using the chain rule.

7. Mar 7, 2015

MarkZone

Thank you very much!

8. Mar 8, 2015

HallsofIvy

Staff Emeritus
Note that, since you have y as a function of x, and x as a function of t, you have, basically, two unknown functions. You will need two independent equations to solve for both x(t) and y(x). That is why Simon Bridge said "where you happen to know dx/dt by some other means"- the "other means" being, essentially, the other equation.