MATH105 April 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q8 (e) • Q8 (f) • Q8 (g) • Q8 (h) • Q8 (i) •
Question 08 (c)
Short-answer questions. No credit will be given for the answer (even if it is correct) without the accompanying work.
Solve the differential equation
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!
First, simplify the right hand side, then use separation of variables.
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We begin by rewriting the equation by using exponent and logarithm rules:
From , we can separate variables:
Now we integrate:
The second integral was solved using the substitution , so that and hence
We can solve for y:
Since C1 is arbitrary, we can just as well write
for C2 an arbitrary constant.
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