57.5.29 problem 15(d)

Internal problem ID [14384]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 15(d)
Date solved : Thursday, October 02, 2025 at 09:35:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {3 t}{3 c_1 \,t^{3}+1} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 24

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

\begin{align*} y(t)&\to \frac {3 t}{1+3 c_1 t^3}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \frac {3 t}{C_{1} t^{3} + 1} \]