Internal problem ID [8419]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 839.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 19
dsolve(diff(y(x),x) = (exp(-y(x)/x)*y(x)+exp(-y(x)/x)*x+x^2)*exp(y(x)/x)/x,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\frac {2 x}{-x^{2}+c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 3.962 (sec). Leaf size: 40
DSolve[y'[x] == (E^(y[x]/x)*(x/E^(y[x]/x) + x^2 + y[x]/E^(y[x]/x)))/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\log (2)-\log \left (-x+\frac {e^{2 c_1}}{x}\right )\right ) \\ y(x)\to -x \log \left (-\frac {x}{2}\right ) \\ \end{align*}