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 : Monday, January 27, 2025 at 07:37:17 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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