Internal problem ID [4415]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sec ^{2}\relax (y)}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.108 (sec). Leaf size: 81
dsolve(diff(y(x),x)=sec(y(x))^2/(1+x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\arcsin \left (\RootOf \left (x^{4} \textit {\_Z} +2 x^{2} \textit {\_Z} +\textit {\_Z} -x^{4} \sin \left (-\textit {\_Z} +4 c_{1}\right )+4 x^{3} \cos \left (-\textit {\_Z} +4 c_{1}\right )+6 x^{2} \sin \left (-\textit {\_Z} +4 c_{1}\right )-4 x \cos \left (-\textit {\_Z} +4 c_{1}\right )-\sin \left (-\textit {\_Z} +4 c_{1}\right )\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.517 (sec). Leaf size: 32
DSolve[y'[x]==Sec[y[x]]^2/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\&\right ][2 \text {ArcTan}(x)+c_1] \\ \end{align*}