Internal problem ID [4923]
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]
\[ \boxed {y^{\prime }-\frac {\sec \left (y\right )^{2}}{x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 81
dsolve(diff(y(x),x)=sec(y(x))^2/(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\arcsin \left (\operatorname {RootOf}\left (\textit {\_Z} +2 x^{2} \textit {\_Z} +\textit {\_Z} \,x^{4}-x^{4} \sin \left (-\textit {\_Z} +4 c_{1} \right )+4 x^{3} \cos \left (-\textit {\_Z} +4 c_{1} \right )+6 x^{2} \sin \left (-\textit {\_Z} +4 c_{1} \right )-4 x \cos \left (-\textit {\_Z} +4 c_{1} \right )-\sin \left (-\textit {\_Z} +4 c_{1} \right )\right )\right )}{2} \]
✓ 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]
\[ y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\&\right ][2 \arctan (x)+c_1] \]