29.7.29 problem 204

Internal problem ID [4804]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 204
Date solved : Monday, January 27, 2025 at 09:40:04 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }+y+2 x \sec \left (y x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)+y(x)+2*x*sec(x*y(x)) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.560 (sec). Leaf size: 19

DSolve[x D[y[x],x]+y[x]+2 x Sec[x y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\arcsin \left (x^2-c_1\right )}{x} \]