Internal problem ID [2584]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (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 \relax (x ) = \frac {\pi }{x} \\ y \relax (x ) = \frac {c_{1}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 49
DSolve[(y[x]+y[x]*Cos[x*y[x]])+(x+x*Cos[x*y[x]])*y'[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*}