Differential equations - help please!

1

1. Use intergration to solve the differential equation:

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

Reply 1

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

5

1) Separate the variables.

2) Just change the words to maths.

The rate of increase of the number of rabbits infected
dx/dt

is proportional to
= k*

the product of the number of rabbits infected and the number not yet infected.
x*(5000-x).

(edited 14 years ago)

Reply 2

RahulMathew

2

Original post

by Jonnislats

1. Use intergration to solve the differential equation:

dx/dt = -1/40(x-15) , x>15

given that x=85 when t=0, expressing t in terms of x.

2. A disease is spreading through a colony of rabbits. There are 5000 rabbits in the colony. At the time t hours, x is the number of rabbits infected. The rate of increase of the number of rabbits infected is proportional to the product of the number of rabbits infected and the number not yet infected.

Formulate a differential equation for dx/dt in terms of variables x and t and a constant of proportionality k.

Thank you!!

Did you get the answer to the first question ?

Reply 3

davros

16

Original post

by RahulMathew

Did you get the answer to the first question ?

This thread is 10 years old and that poster hasn't been active since 2011 so I suspect if they did get an answer it has now drifted out of their consciousness :smile:

Differential equations - help please!

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