Calculating Differential Equations for Exponential Functions

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Homework Help Overview

The discussion revolves around a differential equation related to the rate of change of material in a jar, which is proportional to the square of the amount present, with a given proportionality constant of k=-3. Participants are tasked with writing and solving the differential equation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formulation of the differential equation, with one participant confirming the equation dy/dt=-3y^2. There is an exploration of the separation of variables and integration steps, with questions about the results of these processes.

Discussion Status

The discussion is ongoing, with participants sharing their attempts at solving the differential equation and seeking clarification on the integration process. Some guidance has been offered regarding the manipulation of the equation, but no consensus or final solution has been reached.

Contextual Notes

Participants are working under the constraints of a homework assignment, which includes specific tasks such as writing and solving the differential equation. There is an acknowledgment of uncertainty regarding the integration steps and the constants involved.

joev714
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Homework Statement



The rate of change of the amount of material in a jar is proportional to the square of the amount present with proportionality constant k=-3.

i) Write a differential equation for this situation
ii) Solve the differential equation AND find y if y=1 when t=1/3

Homework Equations


Not sure of the specific equation, but I know it has something to do with exponential equations


The Attempt at a Solution



dy/dt=-3y^2

seperate variables, integrate both sides, That's as far as I got, sorry :[
 
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joev714 said:

Homework Statement



The rate of change of the amount of material in a jar is proportional to the square of the amount present with proportionality constant k=-3.

i) Write a differential equation for this situation
ii) Solve the differential equation AND find y if y=1 when t=1/3

Homework Equations


Not sure of the specific equation, but I know it has something to do with exponential equations


The Attempt at a Solution



dy/dt=-3y^2

seperate variables, integrate both sides, That's as far as I got, sorry :[
Your diff. equation is right. When you separated variables, what did you get?
 
dy/y^2=-3dt

Integrating both sides yielded -1/y=-3t+C
 
joev714 said:
dy/y^2=-3dt

Integrating both sides yielded -1/y=-3t+C
So 1/y = 3t - C = 3t + C*, where C* is just another constant.
Now solve for y.
 

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