50.4.5 problem 5

Internal problem ID [7854]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:26:33 PM
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: 0.016 (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: 0.034 (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*}