# Determining Which Variable Is Independent

1. Jan 23, 2014

### Bashyboy

Hello,

I have a question with regards to solving problems that require knowledge of which variable is dependent and which is independent. Suppose I am presented with the differential equation $x^5 y^{(4)} - x^3 y'' + 6y = 0$; for this differential equation I am asked to determine if it is linear or not. My question does not pertain to linearity, but is, how do I know which variable is the dependent? Is my knowing this solely due to the fact that the equation contains y and its derivatives, or does this not imply that y is the dependent variable?

2. Jan 23, 2014

### Office_Shredder

Staff Emeritus
If there are derivatives of y then it must be dependent on some variable; otherwise what are you differentiating with respect to?

Often the writers are a bit glib in specifying the variable; for example your equation could have x be some arbitrary parameter and y be a function of t, which would change the solutions that you get. Unless specified though if something that looks like a variable (either x or t) appears in the equation then that is typically intended to be the independent variable.
u is