Determining Which Variable Is Independent

In summary, the conversation discusses the process of determining the dependent and independent variables in a differential equation. The speaker also brings up the issue of writers not always specifying the variables clearly. It is stated that if there are derivatives of y, then it must be dependent on some variable, and typically, the variable that appears in the equation is intended to be the independent variable.
  • #1
Bashyboy
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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 [itex]x^5 y^{(4)} - x^3 y'' + 6y = 0[/itex]; 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?
 
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  • #2
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
 
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Related to Determining Which Variable Is Independent

1. What is the definition of an independent variable?

An independent variable is a variable that is manipulated or changed by the researcher in an experiment in order to observe its effect on the dependent variable.

2. How do you determine which variable is independent in an experiment?

The independent variable is usually the variable that the researcher controls or changes in an experiment. It is the variable that is intentionally manipulated to observe its effect on the dependent variable.

3. Can there be more than one independent variable in an experiment?

Yes, there can be more than one independent variable in an experiment. This is known as a multiple independent variable design. In this case, the researcher will manipulate and control more than one variable to observe their combined effects on the dependent variable.

4. What is the difference between an independent variable and a control variable?

An independent variable is the variable that is manipulated by the researcher, while a control variable is a variable that is kept constant throughout the experiment. Control variables are used to ensure that any changes in the dependent variable are solely due to changes in the independent variable and not any other external factors.

5. How do you select the appropriate independent variable for an experiment?

The selection of an appropriate independent variable depends on the research question or hypothesis being investigated. It should be a variable that can be manipulated by the researcher and is directly related to the dependent variable. It is important to carefully choose the independent variable to ensure that the results of the experiment are valid and reliable.

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