Internal problem ID [2205]
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 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact]
Solve \begin {gather*} \boxed {\cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve((cos(x*y(x))-x*y(x)*sin(x*y(x)))-x^2*sin(x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\arccos \left (\frac {c_{1}}{x}\right )}{x} \]
✓ Solution by Mathematica
Time used: 5.51 (sec). Leaf size: 34
DSolve[(Cos[x*y[x]]-x*y[x]*Sin[x*y[x]])-x^2*Sin[x*y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {ArcCos}\left (-\frac {c_1}{x}\right )}{x} \\ y(x)\to \frac {\text {ArcCos}\left (-\frac {c_1}{x}\right )}{x} \\ \end{align*}