Science:Math Exam Resources/Courses/MATH102/December 2013/Question A 08/Statement

Given the differential equation and initial condition

${\frac {dy}{dt}}=y^{2}(y-a),\quad y(0)=2a$

where $a>0$ is a constant, which of the following is true?

(a) $\lim _{t\to \infty }y(t)=0$

(b) $\lim _{t\to \infty }y(t)=\infty$

(c) $\lim _{t\to \infty }y(t)=a$

(d) $\lim _{t\to \infty }y(t)=2a$

(e) None of the above.