50.1.15 problem 15

Internal problem ID [10013]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 06:46:30 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x} \end{align*}

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

ode:=diff(y(x),x) = 1/x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 10

ode=D[y[x],x] == 1/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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