90.2.9 problem 9

Internal problem ID [25060]
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 23
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:48:04 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t y}{1+y} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 13

ode:=diff(y(t),t) = t*y(t)/(1+y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \operatorname {LambertW}\left ({\mathrm e}^{\frac {t^{2}}{2}+c_1}\right ) \]

✓ Mathematica. Time used: 1.141 (sec). Leaf size: 23

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

\begin{align*} y(t)&\to W\left (e^{\frac {t^2}{2}+c_1}\right )\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*y(t)/(y(t) + 1) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = W\left (C_{1} \sqrt {e^{t^{2}}}\right ) \]