40.4.9 problem 19 (j)

Internal problem ID [6649]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (j)
Date solved : Monday, January 27, 2025 at 02:16:52 PM
CAS classification : [_linear]

\begin{align*} r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(r(theta),theta)+(2*r(theta)*cos(theta)+sin(2*theta))=0,r(theta), singsol=all)
 

\[ r = -\sin \left (\theta \right )+\frac {1}{2}+{\mathrm e}^{-2 \sin \left (\theta \right )} c_1 \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 22

DSolve[D[r[t],t]+(2*r[t]*Cos[t]+Sin[2*t])==0,r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to -\sin (t)+c_1 e^{-2 \sin (t)}+\frac {1}{2} \]