Internal problem ID [9204]
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)]`]]
\[ \boxed {y^{\prime }-\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
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)
\[ y \left (x \right ) = \left (2 \ln \left (2\right )+\ln \left (3\right )-\ln \left (\frac {-3 x^{4}-4 x^{3}-12 c_{1} -12 x}{x}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 4.311 (sec). Leaf size: 32
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]
\[ y(x)\to -x \log \left (-\frac {x^3}{4}-\frac {x^2}{3}-\frac {c_1}{x}-1\right ) \]