Internal problem ID [14115]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 15.
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: 16
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: 1.144 (sec). Leaf size: 15
DSolve[(y[x]*Cos[x*y[x]]+Sin[x])+(x*Cos[x*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\arcsin (\cos (x)+c_1)}{x} \]