73.7.28 problem 28

Internal problem ID [15107]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 28
Date solved : Thursday, March 13, 2025 at 05:40:17 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.93 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {1}{3} x W\left (\frac {3 e^{\frac {c_1}{x}}}{x}\right ) \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.605 (sec). Leaf size: 15

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

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