Internal problem ID [5306]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {r^{\prime }+2 r \cos \left (\theta \right )=-\sin \left (2 \theta \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(r(theta),theta)+(2*r(theta)*cos(theta)+sin(2*theta))=0,r(theta), singsol=all)
\[ r \left (\theta \right ) = -\sin \left (\theta \right )+\frac {1}{2}+{\mathrm e}^{-2 \sin \left (\theta \right )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 22
DSolve[r'[t]+(2*r[t]*Cos[t]+Sin[2*t])==0,r[t],t,IncludeSingularSolutions -> True]
\[ r(t)\to -\sin (t)+c_1 e^{-2 \sin (t)}+\frac {1}{2} \]