81.1.30 problem 2-28

Internal problem ID [21475]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-28
Date solved : Thursday, October 02, 2025 at 07:39:24 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 23

ode:=2*x+y(x)+1+(4*x+2*y(x)+3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-10-9 x +9 c_1}\right )}{6}-\frac {5}{3}-2 x \]

✓ Mathematica. Time used: 2.176 (sec). Leaf size: 39

ode=(2*x+y[x]+1)+(4*x+2*y[x]+3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{6} W\left (-e^{-9 x-1+c_1}\right )-2 x-\frac {5}{3}\\ y(x)&\to -2 x-\frac {5}{3} \end{align*}

✓ Sympy. Time used: 0.665 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (4*x + 2*y(x) + 3)*Derivative(y(x), x) + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x - \frac {W\left (C_{1} e^{- 9 x - 10}\right )}{6} - \frac {5}{3} \]