40.2.9 problem 32

Internal problem ID [6587]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 32
Date solved : Sunday, March 30, 2025 at 11:10:45 AM
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: 0.023 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 3.967 (sec). Leaf size: 30

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

✓ Sympy. Time used: 0.872 (sec). Leaf size: 12

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)
 

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