85.34.4 problem 4

Internal problem ID [22712]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 67
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:11:38 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {2}{x +2 y-3} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=diff(y(x),x) = 2/(x+2*y(x)-3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -2 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {x}{4}-\frac {1}{4}}}{4}\right )-\frac {x}{2}-\frac {1}{2} \]

✓ Mathematica. Time used: 60.035 (sec). Leaf size: 34

ode=D[y[x],x]==2/(x+2*y[x]-3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-4 W\left (-\frac {1}{4} c_1 e^{-\frac {x}{4}-\frac {1}{4}}\right )-x-1\right ) \end{align*}

✓ Sympy. Time used: 1.357 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 2/(x + 2*y(x) - 3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{2} - 2 W\left (C_{1} e^{- \frac {x}{4} - \frac {1}{4}}\right ) - \frac {1}{2} \]