88.12.4 problem 4

Internal problem ID [24060]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:56:30 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

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

\[ y = x -\frac {5 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{\frac {x}{5}} c_1 \,{\mathrm e}^{-\frac {8}{5}}}{5}\right )}{2}-4 \]

✓ Mathematica. Time used: 2.257 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 7.336 (sec). Leaf size: 230

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

\[ \left [ y{\left (x \right )} = x - \frac {5 W\left (\frac {2 \sqrt [5]{C_{1} e^{x}}}{5 e^{\frac {8}{5}}}\right )}{2} - 4, \ y{\left (x \right )} = x - \frac {5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (-1 + \sqrt {5} + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {8}{5}}}\right )}{2} - 4, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} - \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {8}{5}}}\right )}{2} - 4, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} + \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {8}{5}}}\right )}{2} - 4, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (- \sqrt {5} + 1 + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {8}{5}}}\right )}{2} - 4\right ] \]