83.4.2 problem 2

Internal problem ID [19003]
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 : 2
Date solved : Monday, March 31, 2025 at 06:31:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

ode:=(2*x+2*y(x)+1)*diff(y(x),x) = x+y(x)+1; 
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: 3.822 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.941 (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)
 

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