90.4.19 problem 20

Internal problem ID [25114]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 20
Date solved : Thursday, October 02, 2025 at 11:50:33 PM
CAS classification : [_separable]

\begin{align*} t y^{\prime }+2 \ln \left (t \right ) y&=4 \ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=t*diff(y(t),t)+2*y(t)*ln(t) = 4*ln(t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 23

ode=t*D[y[t],{t,1}] +2*y[t]*Log[t]== 4*Log[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2+c_1 e^{-\log ^2(t)}\\ y(t)&\to 2 \end{align*}

✓ Sympy. Time used: 0.172 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + 2*y(t)*log(t) - 4*log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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