19.3.3 problem 11

Internal problem ID [3546]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:41:21 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve(sin(y(x)/x)*(x*diff(y(x),x)-y(x))=x*cos(y(x)/x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 26.462 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -x \arccos \left (\frac {e^{-c_1}}{x}\right ) \\ y(x)\to x \arccos \left (\frac {e^{-c_1}}{x}\right ) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}