Final answer:
Without the specific differential equation, we cannot derive solutions, but a general method involves integrating the differential equation. For question 41, the solved equation for focal length is f = di / (di + do). Simultaneous equations are solved through algebraic methods.
Step-by-step explanation:
Without the specific differential equation provided in part 29.a, we are unable to proceed with finding a general solution or a singular solution. However, in general terms, the process to find a general solution involves integrating the differential equation, and applying initial or boundary conditions if they are provided. For the singular solution, one would seek a solution that cannot be derived from the general family of solutions, often by considering the boundary behaviors or constraints that are not applicable to the general solutions.
For question 41, the formula to solve the equation given is f = di / (di + do), assuming the missing operation is division. This rearranges the formula so that the focal length (f) is not represented as a reciprocal. Similarly, solving simultaneous equations typically involves multiple steps of algebra, including substitution, elimination, or using methods like matrix operations.