Solve (17)dD/dt=-ksqrt{D}

$$( 17 ) \frac { d D } { d t } = - k \sqrt { D }$$

Solve for k

$$\left\{\begin{matrix}k=0\text{, }&D\geq 0\\k\in \mathrm{R}\text{, }&D=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\left(-k\right)\sqrt{D}=17\frac{\mathrm{d}}{\mathrm{d}t}(D)$$

Reorder the terms.

$$-\sqrt{D}k=17\frac{\mathrm{d}}{\mathrm{d}t}(D)$$

The equation is in standard form.

$$\left(-\sqrt{D}\right)k=0$$

Divide 0 by -\sqrt{D}.

$$k=0$$

Solve for D

$$\left\{\begin{matrix}\\D=0\text{, }&\text{unconditionally}\\D\geq 0\text{, }&k=0\end{matrix}\right.$$