Question 01 (a)
Solve the following linear ODE:
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.
This is a linear ODE. You may wish to consider an integrating factor.
Given a linear ODE of the form
a suitable integrating factor is
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
Following the hints we multiply the equation by yielding:
Integrating both sides yields
for an arbitrary constant C.
Remark (not part of solution): Technically but by multiplying the entire equation by the integrating factor, we inevitably divide by it and this constant of integration cancels out.