15.7.12 problem 12

Internal problem ID [2993]
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
Date solved : Monday, January 27, 2025 at 07:06:04 AM
CAS classification : [_separable]

\begin{align*} r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 33

dsolve(diff(r(theta),theta)+(r(theta)-1/r(theta))*theta=0,r(theta), singsol=all)
 

\begin{align*} r &= \sqrt {{\mathrm e}^{-\theta ^{2}} c_{1} +1} \\ r &= -\sqrt {{\mathrm e}^{-\theta ^{2}} c_{1} +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.018 (sec). Leaf size: 57

DSolve[D[ r[\[Theta]], \[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*}