83.4.9 problem 9

Internal problem ID [19010]
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 : 9
Date solved : Monday, March 31, 2025 at 06:31:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 23

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

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-9 x -4+9 c_1}\right )}{6}-x -\frac {2}{3} \]

✓ Mathematica. Time used: 3.921 (sec). Leaf size: 39

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

\begin{align*} y(x)\to \frac {1}{6} \left (-W\left (-e^{-9 x-1+c_1}\right )-6 x-4\right ) \\ y(x)\to -x-\frac {2}{3} \\ \end{align*}

✓ Sympy. Time used: 0.967 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = - x - \frac {W\left (C_{1} e^{- 9 x - 4}\right )}{6} - \frac {2}{3} \]