68.6.21 problem 22

Internal problem ID [17331]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 22
Date solved : Thursday, October 02, 2025 at 02:02:56 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 y t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 59

ode:=3*t^2*y(t)+3*y(t)^2-1+(t^3+6*t*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-t^{3}+\sqrt {t \left (t^{5}-12 c_1 +12 t \right )}}{6 t} \\ y &= \frac {-t^{3}-\sqrt {t \left (t^{5}-12 c_1 +12 t \right )}}{6 t} \\ \end{align*}

✓ Mathematica. Time used: 0.364 (sec). Leaf size: 67

ode=(3*t^2*y[t]+3*y[t]^2-1)+(t^3+6*t*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {t^3+\sqrt {t \left (t^5+12 t+36 c_1\right )}}{6 t}\\ y(t)&\to \frac {-t^3+\sqrt {t \left (t^5+12 t+36 c_1\right )}}{6 t} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*y(t) + (t**3 + 6*t*y(t))*Derivative(y(t), t) + 3*y(t)**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out