8.2 problem 1.2-3 (b)

Internal problem ID [2483]

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]

\[ \boxed {t \ln \left (t \right ) y^{\prime }+y=t \ln \left (t \right )} \] With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = 1] \end {align*}

✓ Solution by Maple

Time used: 0.016 (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)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 19

DSolve[{t*Log[t]*y'[t]==t*Log[t]-y[t],y[Exp[1]]==1},y[t],t,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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