44.4.43 problem 25

Internal problem ID [7056]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:42:45 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2} \left (4-y^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 49

dsolve(diff(y(x),x)=y(x)^2*(4-y(x)^2),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}-4\right ) {\mathrm e}^{\textit {\_Z}}+16 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+16 x \,{\mathrm e}^{\textit {\_Z}}-2 \ln \left ({\mathrm e}^{\textit {\_Z}}-4\right )-32 c_{1} +2 \textit {\_Z} -32 x +4\right )}-2 \]

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 57

DSolve[D[y[x],x]==y[x]^2*(4-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{4 \text {$\#$1}}+\frac {1}{16} \log (2-\text {$\#$1})-\frac {1}{16} \log (\text {$\#$1}+2)\&\right ][-x+c_1] \\ y(x)\to -2 \\ y(x)\to 0 \\ y(x)\to 2 \\ \end{align*}