Science:Math Exam Resources/Courses/MATH215/December 2013/Question 07 (b)
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Question 07 (b) 

Consider the following initial value problem for a firstorder autonomous ODE: (b) If , use Euler’s method with step size to approximate the solution at time . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Euler's method is derived by using a tangent line to a solution curve to approximate the value of the solution a time step h later. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We have so that if then We denote y_{0} = 3/2 and t_{0} = 0 so that
Continuing in this process,
