Is this differential equation separable?

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Homework Help Overview

The discussion revolves around determining whether a given differential equation is separable. Participants are examining the properties of the equation and the implications of logarithmic manipulation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of logarithmic laws to analyze the separability of the equation. Questions arise regarding the next steps after applying logarithmic manipulation and how to handle specific terms that may complicate separation.

Discussion Status

Some participants assert that the equation is separable and suggest methods to manipulate it further, while others express confusion about specific terms and seek clarification on the separation process. There is an ongoing exploration of different interpretations of the equation's structure.

Contextual Notes

Participants are working with a visual representation of the equation, which may limit the clarity of certain terms and their relationships. The original poster's question specifically asks about the separability of the equation without providing a full context or additional constraints.

-EquinoX-
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Yes, it is separable. Use the laws of logarithms. ln(s^(5t))=(5t)*ln(s). Now separate it.
 
how do you go on separating it after that? my guess would be:

the 8t^4 confuses me
 
What do you get after you apply the log law? Factor out the t^4. The question is just asking whether it's separable.
 
t^3*(5t)*ln(s) + 8t^4
 
-EquinoX- said:
t^3*(5t)*ln(s) + 8t^4

Well? Keep going. t^3*5*t=5t^4...
 

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