19.1.4 problem 4

Internal problem ID [3518]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:45:38 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

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

\[ y = c_1 \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 15

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

\begin{align*} y(x)\to c_1 \log (x) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} \log {\left (x \right )} \]