The given mathematical expressions from the image are:

1. $y' - 3y + 2y = \frac{1}{3 + e^{-x}}$
2. $y'(1/2) = 1 + 8\ln2$
3. $y' = 4\ln4$

Would you like me to solve the differential equation in (1) or explain any part of the notation? Let me know how you'd like to proceed!

Here are five related questions for deeper understanding:

1. How do you solve first-order linear differential equations?
2. What is the integrating factor method for solving differential equations?
3. How do logarithmic functions affect differentiation?
4. What is the significance of an initial condition like $y'(1/2) = 1 + 8\ln2$?
5. How can we determine if a given differential equation has a unique solution?

Tip: When solving differential equations, always check if they are linear or separable to choose the best solving method.