56.38.7 problem Ex 7

Internal problem ID [14299]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62. Summary. Page 144
Problem number : Ex 7
Date solved : Thursday, October 02, 2025 at 09:30:19 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)+1/x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 13

ode=D[y[x],{x,2}]+1/x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + Derivative(y(x), x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \log {\left (x \right )} \]