90.4.5 problem 6

Internal problem ID [25100]
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 : 6
Date solved : Thursday, October 02, 2025 at 11:50:11 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

\[ y = \frac {c_1 \left (m +1\right )^{2} t^{-m}+t \left (-1+\left (m +1\right ) \ln \left (t \right )\right )}{\left (m +1\right )^{2}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 29

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

\begin{align*} y(t)&\to \frac {t ((m+1) \log (t)-1)}{(m+1)^2}+c_1 t^{-m} \end{align*}

✓ Sympy. Time used: 0.210 (sec). Leaf size: 29

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

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