Internal problem ID [14379]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y-y^{\prime } t=-t} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve([(t+y(t))-t*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = t \left (\ln \left (t \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 11
DSolve[{(t+y[t])-t*y'[t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t (\log (t)+1) \]