15.6.16 problem 16

Internal problem ID [2973]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:05:02 AM
CAS classification : [_linear]

\begin{align*} \cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(cos(theta)*diff(r(theta),theta)=2+2*r(theta)*sin(theta),r(theta), singsol=all)
 

\[ r = \sec \left (\theta \right )^{2} \left (2 \sin \left (\theta \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 17

DSolve[Cos[\[Theta]]*D[ r[\[Theta]], \[Theta] ]==2+2*r[\[Theta]]*Sin[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\[ r(\theta )\to \sec ^2(\theta ) (2 \sin (\theta )+c_1) \]