Internal problem ID [2022]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {r^{\prime }+\left (r-\frac {1}{r}\right ) \theta =0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(r(theta),theta)+(r(theta)-1/r(theta))*theta=0,r(theta), singsol=all)
\begin{align*} r \left (\theta \right ) &= \sqrt {{\mathrm e}^{-\theta ^{2}} c_{1} +1} \\ r \left (\theta \right ) &= -\sqrt {{\mathrm e}^{-\theta ^{2}} c_{1} +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.969 (sec). Leaf size: 57
DSolve[r'[\[Theta]]+(r[\[Theta]]-1/r[\[Theta]])*\[Theta]==0,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to -\sqrt {1+e^{-\theta ^2+2 c_1}} \\ r(\theta )\to \sqrt {1+e^{-\theta ^2+2 c_1}} \\ r(\theta )\to -1 \\ r(\theta )\to 1 \\ \end{align*}