20.5.9 problem Problem 9

Internal problem ID [3692]
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
Date solved : Monday, January 27, 2025 at 07:55:27 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.586 (sec). Leaf size: 17

DSolve[(y[x]*Cos[x*y[x]]-Sin[x])+x*Cos[x*y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\arcsin (-\cos (x)+c_1)}{x} \]