74.7.36 problem 36

Internal problem ID [16113]
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
Date solved : Tuesday, January 28, 2025 at 08:41:59 AM
CAS classification : [_linear]

\begin{align*} t +y-y^{\prime } t&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([(t+y(t))-t*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
 

\[ y = t \left (\ln \left (t \right )+1\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 11

DSolve[{(t+y[t])-t*D[y[t],t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t (\log (t)+1) \]