Download MA1S12: TUTORIAL 6 4x = 0.1 for the initial value problem

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MA1S12: TUTORIAL 6
1. Find the first three approximations given by Euler’s method with
increment 4x = 0.1 for the initial value problem
√
y 0 = x2 y
y(0) = 1
2. The particular solution for the ODE in Q.1. is
y(x) =
2
x3
+1
6
Compute the absolute error for the Euler approximations in Q.1.
3. A petri dish contains bacteria with initial population 100. After 2
hours the population is 110. Assuming an exponential growth model
find the population of the bacteria after 5 hours.
4. A mixing tank contains 300 gallons of water in which 100lbs of salt
has been dissolved. Another mixture of salt and water is pumped
into the tank at a rate of 2 gal/min. The concentration of salt in
this inflow is 1lb per gallon. The resulting mixture is pumped out
of the tank at a rate of 2 gal/min. Find the amount of salt in the
tank after 10 minutes.
1
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