29.16.5 problem 448

Internal problem ID [5046]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 448
Date solved : Tuesday, March 04, 2025 at 07:46:32 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \operatorname {LambertW}\left (-2 c_{1} {\mathrm e}^{-2 x -4}\right )+2 x +4 \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 22

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

\[ y(x)\to W\left (-2 c_1 e^{-2 (x+2)}\right )+2 x+4 \]

✓ Sympy. Time used: 0.782 (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)
 

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