26.2.5 problem 5

Internal problem ID [4254]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 8, page 41
Problem number : 5
Date solved : Monday, January 27, 2025 at 08:45:19 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: 0.022 (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 \left (x \right ) &= \frac {\pi }{x} \\ y \left (x \right ) &= \frac {c_{1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.035 (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*}