Math Problem Statement
MathBio-HUEB-11.pdf
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Solve the excercises.
Solution
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text[:1000]The document contains exercises related to mathematics for biosciences, including differential equations. Here's a summary of the tasks outlined in the first few pages:
Exercise 1:
Solve the initial value problem for , where:
- and ,
- The differential equation is ,
- The initial condition is ,
- Find the solution and the maximum interval on which the solution is defined.
Exercise 2:
Solve the following differential equations and find the maximal interval for each:
- , with initial condition ,
- , with initial condition .
Exercise 3 (Additional):
Solve the SIR model for epidemic spread, given a population of size .
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Initial Value Problems
SIR Model
Formulas
y'(t) = k y(t) ln(S/y(t))
y'(t) = e^t + 4t^3 e^{y(t)}
y'(t) = (2y + 3) (4t + 5)^2
Theorems
Solution of Initial Value Problems
Maximal Interval of Solution
Suitable Grade Level
Undergraduate (Biosciences, Mathematics)
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