(A) What Can You Conclude About the Functions Which Satisfy $y ^ { \prime } = y ^ { 2 }$

question 47

Essay

(a) What can you conclude about the functions which satisfy $y ^ { \prime } = y ^ { 2 }$ just by looking at the differential equation?
(b) Verify that $y = - \frac { 1 } { x + c }$ are solutions of the equation in part (a).
(c) Is there a solution of the equation in part (a) that is not a member of the family of functions in part (b)? Justify your answer.
(d) Find a solution to the equation in part (a) with the additional condition that $y ( 0 ) = \frac { 1 } { 3 }$ .

---

Definitions:

Polygenic Transmission

The process by which multiple genes contribute to the phenotypic expression of a single trait or characteristic in an organism.

Natural Selection

A fundamental mechanism of evolution, where organisms with traits better suited to their environment are more likely to survive and reproduce.

Reproductive Advantage

An evolutionary benefit that leads to an organism having more offspring than others, contributing to its genes being passed on to the next generation.

Necessary Resources

Essential materials, information, or support required for survival, growth, or the accomplishment of a task.