Internal problem ID [8345]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 767.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x) = (-8*x*y(x)-x^3+2*x^2-8*x+32)/(32*y(x)+4*x^2-8*x+32),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{8}+4 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}} {\mathrm e}^{-\frac {3}{4}}}{4}\right )+\frac {x}{4}+3 \]
✓ Solution by Mathematica
Time used: 3.23 (sec). Leaf size: 46
DSolve[y'[x] == (32 - 8*x + 2*x^2 - x^3 - 8*x*y[x])/(32 - 8*x + 4*x^2 + 32*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{8} (x-6) (x+4)+4 W\left (-e^{-\frac {x}{16}-1+c_1}\right ) \\ y(x)\to -\frac {1}{8} (x-6) (x+4) \\ \end{align*}