78.4.4 problem 5

Internal problem ID [18127]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 11:30:06 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

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

\begin{align*} y &= \frac {\pi }{x} \\ y &= \frac {c_1}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 49

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

\begin{align*} y(x)\to -\frac {\pi }{x} \\ y(x)\to \frac {\pi }{x} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to -\frac {\pi }{x} \\ y(x)\to \frac {\pi }{x} \\ \end{align*}