44.4.38 problem 20

Internal problem ID [7051]
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 : 20
Date solved : Monday, January 27, 2025 at 02:42:33 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-y^{4} \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 53

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

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