Internal problem ID [1912]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve(diff(y(x),x)*x-y(x)-x*sin(y(x)/x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\frac {2 x c_{1}}{c_{1}^{2} x^{2}+1}, \frac {-c_{1}^{2} x^{2}+1}{c_{1}^{2} x^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 52
DSolve[y'[x]*x-y[x]-x*Sin[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \arccos (-\tanh (\log (x)+c_1)) \\ y(x)\to x \arccos (-\tanh (\log (x)+c_1)) \\ y(x)\to 0 \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}