89.8.12 problem 14

Internal problem ID [24472]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:40:23 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 2.239 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to 5 W\left (-e^{\frac {x}{5}-1+c_1}\right )+2 x+4\\ y(x)&\to 2 (x+2) \end{align*}

✓ Sympy. Time used: 6.410 (sec). Leaf size: 221

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

\[ \left [ y{\left (x \right )} = 2 x + 5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}}}{5 e^{\frac {4}{5}}}\right ) + 4, \ y{\left (x \right )} = 2 x + 5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} - \sqrt {2} \sqrt {-5 + \sqrt {5}}\right )}{20 e^{\frac {4}{5}}}\right ) + 4, \ y{\left (x \right )} = 2 x + 5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} + \sqrt {2} \sqrt {-5 + \sqrt {5}}\right )}{20 e^{\frac {4}{5}}}\right ) + 4, \ y{\left (x \right )} = 2 x + 5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (- \sqrt {5} + 1 - \sqrt {2} \sqrt {-5 - \sqrt {5}}\right )}{20 e^{\frac {4}{5}}}\right ) + 4, \ y{\left (x \right )} = 2 x + 5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (- \sqrt {5} + 1 + \sqrt {2} \sqrt {-5 - \sqrt {5}}\right )}{20 e^{\frac {4}{5}}}\right ) + 4\right ] \]