(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 $y ( 0 ) = \frac { 1 } { 3 }$ .

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