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 : Monday, January 27, 2025 at 04:35:30 AM
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*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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