44.5.72 problem 61

Internal problem ID [7134]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 61
Date solved : Tuesday, February 04, 2025 at 12:31:52 AM
CAS classification : [_quadrature]

\begin{align*} m^{\prime }&=-\frac {k}{m^{2}} \end{align*}

With initial conditions

\begin{align*} m \left (0\right )&=m_{0} \end{align*}

✗ Solution by Maple

dsolve([diff(m(t),t)= -k/m(t)^2,m(0) = m__0],m(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 62

DSolve[{D[m[t],t]== -k/m[t]^2,{m[0]==m0}},m[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} m(t)\to \sqrt [3]{\text {m0}^3-3 k t} \\ m(t)\to -\sqrt [3]{-1} \sqrt [3]{\text {m0}^3-3 k t} \\ m(t)\to (-1)^{2/3} \sqrt [3]{\text {m0}^3-3 k t} \\ \end{align*}