Internal problem ID [490]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {r^{\prime }-\frac {r^{2}}{x}=0} \end {gather*} With initial conditions \begin {align*} [r \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([diff(r(x),x) = r(x)^2/x,r(1) = 2],r(x), singsol=all)
\[ r \relax (x ) = -\frac {2}{2 \ln \relax (x )-1} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 15
DSolve[{r'[x] == r[x]^2/x,r[1]==2},r[x],x,IncludeSingularSolutions -> True]
\begin{align*} r(x)\to \frac {2}{1-2 \log (x)} \\ \end{align*}