74.8.28 problem 28

Internal problem ID [16093]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 28
Date solved : Monday, March 31, 2025 at 02:41:41 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y-t y^{\prime }&=-2 {y^{\prime }}^{3} \end{align*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 35

ode:=y(t)-t*diff(y(t),t) = -2*diff(y(t),t)^3; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {6}\, t^{{3}/{2}}}{9} \\ y &= \frac {\sqrt {6}\, t^{{3}/{2}}}{9} \\ y &= c_1 \left (-2 c_1^{2}+t \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 56

ode=y[t]-t*D[y[t],t]==-2*D[y[t],t]^3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to c_1 \left (t-2 c_1{}^2\right ) \\ y(t)\to -\frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ y(t)\to \frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*Derivative(y(t), t) + y(t) + 2*Derivative(y(t), t)**3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out