44.5.74 problem 63

Internal problem ID [7136]
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 : 63
Date solved : Tuesday, February 04, 2025 at 12:33:14 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=k \left (A -x\right )^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 18

dsolve([diff(x(t),t)= k*(A-x(t))^2,x(0) = 0],x(t), singsol=all)
 

\[ x = \frac {t k \,A^{2}}{t k A +1} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 19

DSolve[{D[x[t],t]== k*(A-x[t])^2,{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {A^2 k t}{A k t+1} \]