Internal problem ID [2956]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 208.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(x*diff(y(x),x) = y(x)+x*sin(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {2 x c_{1}}{x^{2} c_{1}^{2}+1}, -\frac {x^{2} c_{1}^{2}-1}{x^{2} c_{1}^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 1.737 (sec). Leaf size: 41
DSolve[x y'[x]==y[x]+x Sin[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \text {ArcTan}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ y(x)\to \pi x (-1)^{\left \lfloor \frac {1}{2}-\frac {\arg (x)}{\pi }\right \rfloor } \\ \end{align*}