90.6.6 problem 6

Internal problem ID [25150]
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 : 6
Date solved : Thursday, October 02, 2025 at 11:55:00 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.149 (sec). Leaf size: 42

ode:=2*t*y(t)+(t^2+3*y(t)^2)*diff(y(t),t) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\left (27+3 \sqrt {3 t^{6}+81}\right )^{{2}/{3}}-3 t^{2}}{3 \left (27+3 \sqrt {3 t^{6}+81}\right )^{{1}/{3}}} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out