How to integrate this to solve for Q?

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Homework Help Overview

The discussion revolves around solving a differential equation of the form dQ/dt = 2 - 0.1Q, specifically focusing on how to integrate both sides to find Q.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the integration of both sides of the equation, with one participant questioning the integration of the left side and suggesting it might involve a natural logarithm.

Discussion Status

There is an ongoing exploration of the integration process, with some participants providing guidance on the integration steps while others express uncertainty about specific techniques, such as u-substitution.

Contextual Notes

Participants are navigating the integration of a differential equation without a clear consensus on the method for the left side, indicating potential gaps in understanding or missing information.

Math10
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Homework Statement


How to solve for Q in dQ/dt=2-0.1Q?

Homework Equations


None.

The Attempt at a Solution


dQ/(2-0.1Q)=dt
Now what?
 
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Now integrate both sides and solve for Q.
 
I got t+C after integrating the right side but I don't know how to integrate the left side, is it ln abs(2-0.1Q)?
 
Math10 said:
I got t+C after integrating the right side but I don't know how to integrate the left side, is it ln abs(2-0.1Q)?

Close but not quite. Write out your u substitution for that integral.
 

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