15.3.7 problem 7

Internal problem ID [2900]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 03:07:06 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 3.92 (sec). Leaf size: 33

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

✓ Sympy. Time used: 0.892 (sec). Leaf size: 15

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

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