10.2.12 problem 12

Internal problem ID [1140]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 12
Date solved : Saturday, March 29, 2025 at 10:41:13 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} r \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 14

ode:=diff(r(x),x) = r(x)^2/x; 
ic:=r(1) = 2; 
dsolve([ode,ic],r(x), singsol=all);
 

\[ r = -\frac {2}{2 \ln \left (x \right )-1} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 15

ode=D[ r[x],x] == r[x]^2/x; 
ic=r[1]==2; 
DSolve[{ode,ic},r[x],x,IncludeSingularSolutions->True]
 

\[ r(x)\to \frac {2}{1-2 \log (x)} \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
r = Function("r") 
ode = Eq(Derivative(r(x), x) - r(x)**2/x,0) 
ics = {r(1): 2} 
dsolve(ode,func=r(x),ics=ics)
 

\[ r{\left (x \right )} = - \frac {1}{\log {\left (x \right )} - \frac {1}{2}} \]