05:45

Biocalculus Calculus for the Life Sciences

(a) What can you say about a solution of the equation $y^{\prime}=-y^{2}$ just by looking at the differential equation?

(b) Verify that all members of the family $y=1 /(x+C)$ are solutions of the equation in part (a).

(c) Can you think of a solution of the differential equation $y^{\prime}=-y^{2}$ that is not a member of the family in part (b)?

(d) Find a solution of the initial-value problem

$$y^{\prime}=-y^{2} \quad y(0)=0.5$$