90.5.2 problem 2

Internal problem ID [25121]
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 : 2
Date solved : Thursday, October 02, 2025 at 11:50:47 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 t -3 y}{t -y} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 20

ode:=diff(y(t),t) = (4*t-3*y(t))/(t-y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t \left (2 \operatorname {LambertW}\left (c_1 t \right )+1\right )}{\operatorname {LambertW}\left (c_1 t \right )} \]

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 33

ode=D[y[t],{t,1}] ==(4*t-3*y[t])/(t-y[t]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\log \left (\frac {y(t)}{t}-2\right )-\frac {1}{\frac {y(t)}{t}-2}=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (4*t - 3*y(t))/(t - y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

RecursionError : maximum recursion depth exceeded