Internal problem ID [2668]
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]
\[ \boxed {\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )-x \cos \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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: 25.367 (sec). Leaf size: 56
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 \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*}