74.7.48 problem 51

Internal problem ID [16054]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 51
Date solved : Monday, March 31, 2025 at 02:37:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 35

ode:=t*diff(y(t),t)-diff(y(t),t)^3 = y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= -\frac {2 \sqrt {3}\, t^{{3}/{2}}}{9} \\ y &= \frac {2 \sqrt {3}\, t^{{3}/{2}}}{9} \\ y &= c_1 \left (-c_1^{2}+t \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 52

ode=t*D[y[t],t]-D[y[t],t]^3==y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to c_1 \left (t-c_1{}^2\right ) \\ y(t)\to -\frac {2 t^{3/2}}{3 \sqrt {3}} \\ y(t)\to \frac {2 t^{3/2}}{3 \sqrt {3}} \\ \end{align*}

✗ Sympy

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

Timed Out