63.4.10 problem 4(b)

Internal problem ID [13053]
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)
Date solved : Tuesday, January 28, 2025 at 04:50:17 AM
CAS classification : [_separable]

\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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: 0.284 (sec). Leaf size: 34

DSolve[D[ theta[t],t]==t*Sqrt[1+t^2]*Sec[theta[t]],theta[t],t,IncludeSingularSolutions -> True]
 

\[ \theta (t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\frac {1}{3} \left (t^2+1\right )^{3/2}+c_1\right ] \]