76.1.16 problem 16

Internal problem ID [17315]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 09:59:45 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 15

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

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