Internal problem ID [3464]
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]
\[ \boxed {x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )=0} \]
✓ 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)
\[ y \left (x \right ) = \arctan \left (\frac {2 x c_{1}}{c_{1}^{2} x^{2}+1}, -\frac {c_{1}^{2} x^{2}-1}{c_{1}^{2} x^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.325 (sec). Leaf size: 52
DSolve[x y'[x]==y[x]+x Sin[y[x]/x],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*}