Internal problem ID [3056]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \sec \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x)=x*sec(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {x^{2}}{2}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.436 (sec). Leaf size: 31
DSolve[y'[x]==x*Sec[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {x^2}{2}+c_1\right ) y(x)\to \arcsin \left (\frac {x^2}{2}+c_1\right ) \end{align*}