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

Given the differential equation and initial condition

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

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

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

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

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

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

(e) None of the above.