68.6.15 problem 16

Internal problem ID [17325]
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 : 16
Date solved : Thursday, October 02, 2025 at 02:02:35 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational]

\begin{align*} -\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=-1/y(t)+(t/y(t)^2+3*y(t)^2)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ -y^{4}-y c_1 +t = 0 \]

✓ Mathematica. Time used: 60.079 (sec). Leaf size: 1073

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 1.136 (sec). Leaf size: 935

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

\[ \text {Solution too large to show} \]