74.8.27 problem 27

Internal problem ID [16092]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 27
Date solved : Monday, March 31, 2025 at 02:41:38 PM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} y-t y^{\prime }&=2 y^{2} \ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \frac {t}{2 t \ln \left (t \right )-2 t +c_1} \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 25

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

\begin{align*} y(t)\to \frac {t}{-2 t+2 t \log (t)+c_1} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.226 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = \frac {t}{C_{1} + 2 t \log {\left (t \right )} - 2 t} \]