Internal problem ID [7791]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 211.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } y-x \,{\mathrm e}^{\frac {x}{y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 31
dsolve(y(x)*diff(y(x),x)-x*exp(x/y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{-\textit {\_a}^{2}+{\mathrm e}^{\frac {1}{\textit {\_a}}}}d \textit {\_a} \right )+\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 41
DSolve[y[x]*y'[x]-x*Exp[x/y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{K[1]^2-e^{\frac {1}{K[1]}}}dK[1]=-\log (x)+c_1,y(x)\right ] \]