69.4.19 problem 81

Internal problem ID [18008]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 81
Date solved : Thursday, October 02, 2025 at 02:33:16 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 7

ode:=diff(y(x),x) = y(x)/x; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = c_1 x \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

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

✗ Sympy

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

ValueError : Couldnt solve for initial conditions