Internal problem ID [11377]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises
page 26
Problem number: 4(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\theta ^{\prime }-t \sqrt {t^{2}+1}\, \sec \left (\theta \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(theta(t),t)=t*sqrt(1+t^2)*sec(theta(t)),theta(t), singsol=all)
\[ \theta \left (t \right ) = \arcsin \left (\frac {t^{2} \sqrt {t^{2}+1}}{3}+\frac {\sqrt {t^{2}+1}}{3}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 5.052 (sec). Leaf size: 91
DSolve[theta'[t]==t*Sqrt[1+t^2]*Sec[theta[t]],theta[t],t,IncludeSingularSolutions -> True]
\begin{align*} \theta (t)\to \arcsin \left (\frac {1}{3} \left (\sqrt {t^2+1} t^2+\sqrt {t^2+1}+3 c_1\right )\right ) \\ \theta (t)\to \arcsin \left (\frac {1}{3} \left (\sqrt {t^2+1} t^2+\sqrt {t^2+1}+3 c_1\right )\right ) \\ \theta (t)\to \arcsin \left (\frac {1}{3} \left (t^2+1\right )^{3/2}\right ) \\ \end{align*}