Internal problem ID [2212]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page
91
Problem number: Problem 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y \cos \left (y x \right )-\sin \relax (x )+x \cos \left (y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 14
dsolve((y(x)*cos(x*y(x))-sin(x))+x*cos(x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\arcsin \left (\cos \relax (x )+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.475 (sec). Leaf size: 17
DSolve[(y[x]*Cos[x*y[x]]-Sin[x])+x*Cos[x*y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {ArcSin}(-\cos (x)+c_1)}{x} \\ \end{align*}