90.6.4 problem 4

Internal problem ID [25148]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 83
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:54:49 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

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

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

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 46

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

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

✓ Sympy. Time used: 0.274 (sec). Leaf size: 26

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

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