15.3.19 problem 19

Internal problem ID [2912]
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 : 19
Date solved : Sunday, March 30, 2025 at 12:53:25 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y+\left (4 x +2 y+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-\frac {1}{6}\right )&=0 \end{align*}

✓ Maple. Time used: 0.205 (sec). Leaf size: 21

ode:=2*x+y(x)+(4*x+2*y(x)+1)*diff(y(x),x) = 0; 
ic:=y(-1/6) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-1, -2 \,{\mathrm e}^{-\frac {7}{2}-9 x}\right )}{6}-\frac {2}{3}-2 x \]

✗ Mathematica

ode=(2*x+y[x])+(4*x+2*y[x]+1)*D[y[x],x]==0; 
ic={y[-1/6]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (4*x + 2*y(x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {y(-1/6): 0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions