90.5.18 problem 19

Internal problem ID [25137]
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 : 19
Date solved : Thursday, October 02, 2025 at 11:53:45 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{2 t -2 y+1} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=diff(y(t),t) = 1/(2*t-2*y(t)+1); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 60.027 (sec). Leaf size: 21

ode=D[y[t],{t,1}] == 1/(2*t-2*y[t]+1); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t-\frac {1}{2} W\left (2 c_1 e^{2 t}\right ) \end{align*}

✓ Sympy. Time used: 0.455 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - 1/(2*t - 2*y(t) + 1),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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