Consider the Differential Equation Y' = Y - $y ^ { 2 }$

Multiple Choice

Consider the differential equation y' = y - $y ^ { 2 }$ . Which of the following statements is/are true?

A) The function f(t) = $\frac { 1 } { \left( 1 + e ^ { - t } \right) }$ is a solution to this differential equation with initial condition $y ( 0 ) = \frac { 1 } { 2 }$
B) This differential equation has infinitely many solutions.
C) The constant function f(t) = 1 is a solution to this differential equation.
D) If f(t) is a solution to the differential equation satisfying the initial condition y(0) = 0, then $f ^ { \prime } ( 0 ) = 0$
E) All of these statements are true.