20.4.8 problem Problem 16

Internal problem ID [3643]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 16
Date solved : Tuesday, March 04, 2025 at 04:58:02 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.225 (sec). Leaf size: 24

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

\begin{align*} y(x)\to x e^{1+e^{c_1} x} \\ y(x)\to e x \\ \end{align*}

✓ Sympy. Time used: 0.868 (sec). Leaf size: 10

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

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