MATH103 April 2009
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Question 03 (b)
Consider the differential equation
Find the solution with the initial condition x(0) = 2.
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!
Use your solution from part (a):
Does the initial condition dictate a positive or a negative sign for x(t)?
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.
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Recall the solution from part (a):
To satisfy the initial condition , we calculate
We see, that this can only be fullfilled with the plus sign.
So, the solution of the differential equation with initial condition is
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