15.3.14 problem 14

Internal problem ID [2907]
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 : 14
Date solved : Sunday, March 30, 2025 at 12:53:02 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.164 (sec). Leaf size: 20

ode:=x+y(x)+4 = (2*x+2*y(x)-1)*diff(y(x),x); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -x -\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-x -\frac {2}{3}}}{3}\right )}{2}-1 \]

✓ Mathematica. Time used: 3.206 (sec). Leaf size: 28

ode=(x+y[x]+4)==(2*x+2*y[x]-1)*D[y[x],x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3}{2} W\left (-\frac {2}{3} e^{-x-\frac {2}{3}}\right )-x-1 \]

✓ Sympy. Time used: 1.443 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (2*x + 2*y(x) - 1)*Derivative(y(x), x) + y(x) + 4,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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