74.4.35 problem 35

Internal problem ID [15928]
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
Date solved : Tuesday, January 28, 2025 at 08:23:05 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{3}+1 \end{align*}

✓ Solution by Maple

Time used: 1.141 (sec). Leaf size: 51

dsolve(diff(y(t),t)=y(t)^3+1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 63

DSolve[D[y[t],t]==y[t]^3+1,y[t],t,IncludeSingularSolutions -> True]
 

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