68.1.23 problem 30

Internal problem ID [17090]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 30
Date solved : Thursday, October 02, 2025 at 01:42:56 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 53

ode:=3*y(t)*(t^2+y(t))+t*(t^2+6*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 \right )}}{6 t} \\ y &= \frac {-t^{3}-\sqrt {t \left (t^{5}+12 c_1 \right )}}{6 t} \\ \end{align*}

✓ Mathematica. Time used: 0.311 (sec). Leaf size: 59

ode=3*y[t]*(t^2+y[t])+t*(t^2+6*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^6+36 c_1 t}}{6 t}\\ y(t)&\to \frac {-t^3+\sqrt {t^6+36 c_1 t}}{6 t} \end{align*}

✓ Sympy. Time used: 5.858 (sec). Leaf size: 39

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

\[ \left [ y{\left (t \right )} = \frac {t^{2} \left (\sqrt {\frac {C_{1}}{t^{5}} + 1} - 1\right )}{6}, \ y{\left (t \right )} = - \frac {t^{2} \left (\sqrt {\frac {C_{1}}{t^{5}} + 1} + 1\right )}{6}\right ] \]