76.5.15 problem 15

Internal problem ID [17364]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 15
Date solved : Monday, March 31, 2025 at 04:07:48 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = \frac {1}{\left (-\ln \left (t \right )+c_1 \right ) t^{3}} \]

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.220 (sec). Leaf size: 12

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

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