83.4.23 problem 23

Internal problem ID [19024]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 23
Date solved : Monday, March 31, 2025 at 06:33:43 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 3.06 (sec). Leaf size: 31

ode=(x-y[x]-2)-(2*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^{-x-1+c_1}\right )+x-1 \\ y(x)\to x-1 \\ \end{align*}

✓ Sympy. Time used: 1.009 (sec). Leaf size: 15

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

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