55.1.1 problem HW 1 problem 6(a)

Internal problem ID [8697]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : HW 1 problem 6(a)
Date solved : Wednesday, March 05, 2025 at 06:12:40 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)/x/ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.029 (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: 0.211 (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)
 

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