Internal problem ID [2014]
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: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )=t \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(sin(theta(t))*diff(theta(t),t)+(cos(theta(t))-t*exp(-t) )=0,theta(t), singsol=all)
\[ \theta \left (t \right ) = \arccos \left (\frac {\left (1+2 t \right ) {\mathrm e}^{-t}}{4}+{\mathrm e}^{t} c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 21.418 (sec). Leaf size: 59
DSolve[Sin[\[Theta][t]]*\[Theta]'[t]+(Cos[\[Theta][t]]-t*Exp[-t] )==0,\[Theta][t],t,IncludeSingularSolutions -> True]
\begin{align*} \theta (t)\to -\arccos \left (\frac {1}{4} e^{-t} \left (2 t+4 c_1 e^{2 t}+1\right )\right ) \\ \theta (t)\to \arccos \left (\frac {1}{4} e^{-t} \left (2 t+4 c_1 e^{2 t}+1\right )\right ) \\ \end{align*}