Calculating Differential Equations for Exponential Functions

[joev714]

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 :[

 

[Mark44]

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?

 

[joev714]

dy/y^2=-3dt

Integrating both sides yielded -1/y=-3t+C

 

[Mark44]

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.