Internal problem ID [9096]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 761.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve(diff(y(x),x) = (-4*x*y(x)-x^3+4*x^2-4*x+8)/(8*y(x)+2*x^2-8*x+8),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{4}+\operatorname {LambertW}\left ({\mathrm e}^{-x} c_{1} \right )+x \]
✓ Solution by Mathematica
Time used: 3.739 (sec). Leaf size: 38
DSolve[y'[x] == (8 - 4*x + 4*x^2 - x^3 - 4*x*y[x])/(8 - 8*x + 2*x^2 + 8*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (-e^{-x-1+c_1}\right )-\frac {x^2}{4}+x \\ y(x)\to -\frac {1}{4} (x-4) x \\ \end{align*}