Internal problem ID [8450]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 870.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x) = (exp(-y(x)/x)*y(x)+exp(-y(x)/x)*x+x+x^3+x^4)*exp(y(x)/x)/x,y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (-\frac {3 x^{4}+4 x^{3}+12 x +12 c_{1}}{12 x}\right ) x \]
✓ Solution by Mathematica
Time used: 4.088 (sec). Leaf size: 30
DSolve[y'[x] == (E^(y[x]/x)*(x + x/E^(y[x]/x) + x^3 + x^4 + y[x]/E^(y[x]/x)))/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \log \left (-\frac {1}{12} (3 x+4) x^2-\frac {c_1}{x}-1\right ) \\ \end{align*}