Internal problem ID [2159]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\sin \left (\frac {y}{x}\right ) \left (y^{\prime } x -y\right )-x \cos \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (x ) = x \arccos \left (\frac {1}{x c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 22.627 (sec). Leaf size: 48
DSolve[Sin[y[x]/x]*(x*y'[x]-y[x])==x*Cos[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sec ^{-1}\left (e^{c_1} x\right ) \\ y(x)\to x \sec ^{-1}\left (e^{c_1} x\right ) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}