1.5 problem 5

Internal problem ID [2547]

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]

Solve \begin {gather*} \boxed {y^{\prime }-x \sec \relax (y)=0} \end {gather*}

Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

dsolve(diff(y(x),x)=x*sec(y(x)),y(x), singsol=all)
 

\[ y \relax (x ) = \arcsin \left (\frac {x^{2}}{2}+c_{1}\right ) \]

Solution by Mathematica

Time used: 0.35 (sec). Leaf size: 31

DSolve[y'[x]==x*Sec[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {ArcSin}\left (\frac {x^2}{2}+c_1\right ) \\ y(x)\to \text {ArcSin}\left (\frac {x^2}{2}+c_1\right ) \\ \end{align*}