Internal problem ID [2721]
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)]`]]
\[ \boxed {y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {\arcsin \left (\cos \left (x \right )+c_{1} \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.628 (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]
\[ y(x)\to \frac {\arcsin (-\cos (x)+c_1)}{x} \]