In this question, you will solve the differential equation % o35 _ 0, This differential equation Is separable, in other words, we can write it in the form % = p(8) aly) What are the two functions p() and g(y)? Pty =2 9 alv) =] e> L4 Now separate the variables. Integrate both sides of the resulting equation with respect to t and replace %dr by dy in the integral on the left side. ; dy S j oY Y / _9 dt L 4 Do the integrations an both sides. Use & to stand for your constant of integration for the left side and & to stand for your constant of integration for the right side. (Lower case k on left side, upper case X on right side.) Integrating left side gives: Integrating right side gives: We can combine the two constants of integration into a single constant, C, that appears as +C on the right side of our equation. (We do this by subtracting k from both sides of the equation.) Write the new constant C in terms of k and K c=|Kk v Note: For the rest of this problem and for all problems following in this assignment, whenever we do separation of variables, we will use a single constant of integration, adding C to the right side. Even i wrote A = ein an example in class), you should leave your answer in terms of C. Finally, rearrange to get y as a function of t. (The constant of integration, C, will appear in your answer.) is possible to simplify (like, for instance, when we