17.8.2 problem 1.2-3 (b)

Internal problem ID [3454]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (b)
Date solved : Tuesday, March 04, 2025 at 04:39:47 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=1 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 18

ode:=t*ln(t)*diff(y(t),t) = t*ln(t)-y(t); 
ic:=y(exp(1)) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 19

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

\[ y(t)\to \frac {-t+t \log (t)+1}{\log (t)} \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*log(t)*Derivative(y(t), t) - t*log(t) + y(t),0) 
ics = {y(E): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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