Internal problem ID [3469]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 213.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-y-x \,{\mathrm e}^{\frac {y}{x}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(x*diff(y(x),x) = y(x)+x*exp(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-\frac {1}{\ln \left (x \right )+c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 18
DSolve[x y'[x]==y[x]+x Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \log (-\log (x)-c_1) \]