20.5.2 problem Problem 2

Internal problem ID [3685]
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
Date solved : Monday, January 27, 2025 at 07:55:22 AM
CAS classification : [[_homogeneous, `class G`], _exact]

\begin{align*} \cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime }&=0 \end{align*}

✓ 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)
 

\[ y \left (x \right ) = \frac {\arccos \left (\frac {c_{1}}{x}\right )}{x} \]

✓ Solution by Mathematica

Time used: 5.369 (sec). Leaf size: 34

DSolve[(Cos[x*y[x]]-x*y[x]*Sin[x*y[x]])-x^2*Sin[x*y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\arccos \left (-\frac {c_1}{x}\right )}{x} \\ y(x)\to \frac {\arccos \left (-\frac {c_1}{x}\right )}{x} \\ \end{align*}