Internal problem ID [14193]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{3}=1} \]
✓ Solution by Maple
Time used: 0.563 (sec). Leaf size: 51
dsolve(diff(y(t),t)=y(t)^3+1,y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{2}+\frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\sqrt {3}+\tan \left (\textit {\_Z} \right )\right )+6 \sqrt {3}\, c_{1} +6 \sqrt {3}\, t -6 \textit {\_Z} \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 80
DSolve[y'[t]==y[t]^3+1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [-\frac {1}{6} \log \left (\text {$\#$1}^2-\text {$\#$1}+1\right )+\frac {\arctan \left (\frac {2 \text {$\#$1}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\frac {1}{3} \log (\text {$\#$1}+1)\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to \sqrt [3]{-1} \\ y(t)\to -(-1)^{2/3} \\ \end{align*}