74.4.35 problem 35

Internal problem ID [15857]
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 : Monday, March 31, 2025 at 02:02:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.174 (sec). Leaf size: 51

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

\[ y = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\tan \left (\textit {\_Z} \right )+\sqrt {3}\right )+6 \sqrt {3}\, c_1 +6 \sqrt {3}\, t -6 \textit {\_Z} \right )\right )}{2}+\frac {1}{2} \]

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

ode=D[y[t],t]==y[t]^3+1; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.581 (sec). Leaf size: 46

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**3 + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ t - \frac {\log {\left (y{\left (t \right )} + 1 \right )}}{3} + \frac {\log {\left (y^{2}{\left (t \right )} - y{\left (t \right )} + 1 \right )}}{6} - \frac {\sqrt {3} \operatorname {atan}{\left (\frac {\sqrt {3} \left (2 y{\left (t \right )} - 1\right )}{3} \right )}}{3} = C_{1} \]