Internal problem ID [2952]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 204.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime } x +y+2 x \sec \left (y x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+y(x)+2*x*sec(x*y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\arcsin \left (-x^{2}+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.393 (sec). Leaf size: 19
DSolve[x y'[x]+y[x]+2 x Sec[x y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {ArcSin}\left (x^2-c_1\right )}{x} \\ \end{align*}