74.1.23 problem 30

Internal problem ID [15732]
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 : Monday, March 31, 2025 at 01:46:25 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: 0.020 (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: 0.003 (sec). Leaf size: 114

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

\begin{align*} y(t)\to \frac {1}{6} \left (-\sqrt {3} \sqrt {t^2 \left (3 t^2+8 t y''(x)+12 y''(x)^2\right )}-3 t^2-6 t y''(x)\right ) \\ y(t)\to \frac {1}{6} \left (\sqrt {3} \sqrt {t^2 \left (3 t^2+8 t y''(x)+12 y''(x)^2\right )}-3 t^2-6 t y''(x)\right ) \\ \end{align*}

✓ Sympy. Time used: 8.999 (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 + y(t))*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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