56.1.13 problem 13

Internal problem ID [8725]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 13
Date solved : Sunday, March 30, 2025 at 01:25:05 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 y}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 9

ode:=diff(y(x),x) = 2*y(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 7

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

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