89.8.6 problem 6

Internal problem ID [24466]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:39:54 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

\[ y = \operatorname {LambertW}\left (-2 c_1 \,{\mathrm e}^{-2 x -4}\right )+2 x +4 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to W\left (-2 c_1 e^{-2 (x+2)}\right )+2 x+4 \end{align*}

✓ Sympy. Time used: 0.492 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = 2 x + W\left (C_{1} e^{- 2 x - 4}\right ) + 4 \]