Science:Math Exam Resources/Courses/MATH101 A/April 2024/Question 08
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Question 08 |
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Find the general solution of 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! |
Hint |
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A useful approach is to recognize that this is a separable differential equation, meaning that all the terms involving can be written on one side and all the terms involving can be written on the other. |
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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Solution |
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Since the given differential equation is separable, we can separate the variables and integrate both sides as follows
Now, we can solve for by taking the natural logarithm of both sides
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