Internal problem ID [13290]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{3}=8} \]
✓ Solution by Maple
Time used: 0.516 (sec). Leaf size: 50
dsolve(diff(y(x),x)-y(x)^3=8,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\sqrt {3}+\tan \left (\textit {\_Z} \right )\right )+24 \sqrt {3}\, c_{1} +24 \sqrt {3}\, x -6 \textit {\_Z} \right )\right )+1 \]
✓ Solution by Mathematica
Time used: 0.206 (sec). Leaf size: 83
DSolve[y'[x]-y[x]^3==8,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {1}{24} \log \left (\text {$\#$1}^2-2 \text {$\#$1}+4\right )+\frac {\arctan \left (\frac {\text {$\#$1}-1}{\sqrt {3}}\right )}{4 \sqrt {3}}+\frac {1}{12} \log (\text {$\#$1}+2)\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 2 \sqrt [3]{-1} \\ y(x)\to -2 (-1)^{2/3} \\ \end{align*}