58.7.8 problem 8

Internal problem ID [14663]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:49:04 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 23

ode:=3*x-y(x)+1-(6*x-2*y(x)-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{5 x -4-5 c_1}\right )}{2}+3 x -2 \]

✓ Mathematica. Time used: 2.124 (sec). Leaf size: 35

ode=(3*x-y[x]+1)-(6*x-2*y[x]-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} W\left (-e^{5 x-1+c_1}\right )+3 x-2\\ y(x)&\to 3 x-2 \end{align*}

✓ Sympy. Time used: 0.690 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - (6*x - 2*y(x) - 3)*Derivative(y(x), x) - y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x - \frac {W\left (C_{1} e^{5 x - 4}\right )}{2} - 2 \]