90.5.24 problem 25

Internal problem ID [25143]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 25
Date solved : Thursday, October 02, 2025 at 11:54:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }+y \ln \left (y\right )&=y t \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 14

ode:=diff(y(t),t)+y(t)*ln(y(t)) = t*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{{\mathrm e}^{-t} c_1 -1+t} \]

✓ Mathematica. Time used: 0.152 (sec). Leaf size: 20

ode=D[y[t],{t,1}] +y[t]*Log[y[t]] == t*y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{t-e^{-t+c_1}-1} \end{align*}

✓ Sympy. Time used: 0.451 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*y(t) + y(t)*log(y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = e^{C_{1} e^{- t} + t - 1} \]