68.6.19 problem 20

Internal problem ID [17329]
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 : 20
Date solved : Thursday, October 02, 2025 at 02:02:50 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

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

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

✓ Mathematica. Time used: 0.141 (sec). Leaf size: 60

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

\begin{align*} y(t)&\to -\frac {\sqrt {-t^3+3 c_1}}{\sqrt {3} \sqrt {t}}\\ y(t)&\to \frac {\sqrt {-t^3+3 c_1}}{\sqrt {3} \sqrt {t}} \end{align*}

✓ Sympy. Time used: 0.315 (sec). Leaf size: 39

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

\[ \left [ y{\left (t \right )} = - \frac {\sqrt {3} \sqrt {\frac {C_{1}}{t} - t^{2}}}{3}, \ y{\left (t \right )} = \frac {\sqrt {3} \sqrt {\frac {C_{1}}{t} - t^{2}}}{3}\right ] \]