Internal problem ID [1974]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-3, page 12
Problem number: 1.2-3 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {t \ln \relax (t ) y^{\prime }-\ln \relax (t ) t +y=0} \end {gather*} With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (t ) = \frac {1+\left (\ln \relax (t )-1\right ) t}{\ln \relax (t )} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 17
DSolve[{t*Log[t]*y'[t]==t*Log[t]-y[t],y[Exp[1]]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t+\frac {1-t}{\log (t)} \\ \end{align*}