73.2.3 problem 3.4 c

Internal problem ID [15026]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 c
Date solved : Tuesday, January 28, 2025 at 07:27:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-y^{3}&=8 \end{align*}

✓ Solution by Maple

Time used: 1.142 (sec). Leaf size: 50

dsolve(diff(y(x),x)-y(x)^3=8,y(x), singsol=all)
 

\[ y = 1+\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\tan \left (\textit {\_Z} \right )+\sqrt {3}\right )+24 \sqrt {3}\, c_{1} +24 \sqrt {3}\, x -6 \textit {\_Z} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 65

DSolve[D[y[x],x]-y[x]^3==8,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]+2) \left (K[1]^2-2 K[1]+4\right )}dK[1]\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 2 \sqrt [3]{-1} \\ y(x)\to -2 (-1)^{2/3} \\ \end{align*}