Chapter 3.2, Problem 29E

(a)

To determine

The solution of the differential equation $\frac{dy}{dx}=\frac{v_{s}y-v_r\sqrt{x^2+y^2}}{v_{s}x}$ with the initial condition $y\left(1\right)=0$.

(b)

To determine

The value of $v_s$ for which the swimmer will reach the point $\left(0,0\right)$ by examining $\underset{x\to 0}{\lim }y\left(x\right)$ in the cases $k=1$, $k>1$ and $0<k<1$.