Two differential equation questions
Hey i've been studying over my extension math revision and i just cant get my head around these two questions. I'm sure i've been setting up the differential equations wrong but im not sure whats right. i have been for q1, dr/dt = y^(1/2). fliping to dt/dr then intergrating
just some assitance with setting up the begining equation will be enough to get me going its just the start of these i get confused about
The test is tomorow and tuesday so im kind of freaking out. heres the two questions, thanks in advance.
1. Oil is leaking out of a barrel loaded in a cargo ship. The rate at which the oil level is dropping seems proportional to the square root of the level of oil in the barrel at that time.
Write a differential equation for y(t), the level of oil (in cms) and time (hours).
Find a general solution for the equation.
If the barrel was filled up to 144cm when it started leaking and the level dropped to 80cm in four hours, how long will it take for the barrel to empty?
2. An investigation is under way in the department of forests, land and conservation to improve our understanding of the rate at which bush fires spread. A bush fire has broken out and a spotter plane has already taken some photographs. The first photograph shows a fire area of half a hectare. Comparison with a photograph taken six hours later shows that the fire seems to be spreading uniformly in all directions and has burned an additional 1700 square metres.
Use differential equations and find two possible models for the spread of the fire.