75.2.18 problem 38

Internal problem ID [16624]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 38
Date solved : Monday, March 31, 2025 at 03:01:55 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]
 

\[ y(x)\to \log (x)+c_1 \]

✓ Sympy. Time used: 0.179 (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)
 

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