44.4.41 problem 23

Internal problem ID [7054]
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 : 23
Date solved : Monday, January 27, 2025 at 02:42:41 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 116

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

\begin{align*} y &= \frac {3^{{2}/{3}} \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}+6 c_{1} +6 x}{3 c_{1} +3 x} \\ y &= \frac {\left (-3 i 3^{{1}/{6}}-3^{{2}/{3}}\right ) \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}+12 x +12 c_{1}}{6 x +6 c_{1}} \\ y &= \frac {\left (3 i 3^{{1}/{6}}-3^{{2}/{3}}\right ) \left (-\left (x +c_{1} \right )^{2}\right )^{{1}/{3}}+12 x +12 c_{1}}{6 x +6 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.784 (sec). Leaf size: 133

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

\begin{align*} y(x)\to \frac {1}{3} \left (6-\frac {3^{2/3} \sqrt [3]{(x+c_1){}^2}}{x+c_1}\right ) \\ y(x)\to \frac {12 x+\sqrt [6]{3} \left (\sqrt {3}-3 i\right ) \sqrt [3]{(x+c_1){}^2}+12 c_1}{6 (x+c_1)} \\ y(x)\to \frac {12 x+\sqrt [6]{3} \left (\sqrt {3}+3 i\right ) \sqrt [3]{(x+c_1){}^2}+12 c_1}{6 (x+c_1)} \\ y(x)\to 2 \\ \end{align*}