Internal problem ID [3470]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 214.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x*diff(y(x),x) = x+y(x)+x*exp(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\ln \left (-\frac {x}{x \,{\mathrm e}^{c_{1}}-1}\right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 4.516 (sec). Leaf size: 38
DSolve[x y'[x]==x+y[x]+x Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log \left (\frac {1}{2} \left (-1+\tanh \left (\frac {1}{2} (-\log (x)-c_1)\right )\right )\right ) y(x)\to i \pi x \end{align*}