Internal problem ID [8529]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 949.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+x y+x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 97
dsolve(diff(y(x),x) = (x^2*y(x)+x^4+2*x^3-3*x^2+x*y(x)+x+y(x)^3+3*x^2*y(x)^2-3*x*y(x)^2+3*y(x)*x^4-6*x^3*y(x)+x^6-3*x^5)/x/(y(x)+x^2-x+1),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {c_{1}-2 \ln \relax (x )}\, x^{2}-\sqrt {c_{1}-2 \ln \relax (x )}\, x -x^{2}+x -1}{-1+\sqrt {c_{1}-2 \ln \relax (x )}} \\ y \relax (x ) = -\frac {\sqrt {c_{1}-2 \ln \relax (x )}\, x^{2}-\sqrt {c_{1}-2 \ln \relax (x )}\, x +x^{2}-x +1}{1+\sqrt {c_{1}-2 \ln \relax (x )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.458 (sec). Leaf size: 65
DSolve[y'[x] == (x - 3*x^2 + 2*x^3 + x^4 - 3*x^5 + x^6 + x*y[x] + x^2*y[x] - 6*x^3*y[x] + 3*x^4*y[x] - 3*x*y[x]^2 + 3*x^2*y[x]^2 + y[x]^3)/(x*(1 - x + x^2 + y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2+x+\frac {1}{-1+\sqrt {-2 \log (x)+c_1}} \\ y(x)\to -x^2+x-\frac {1}{1+\sqrt {-2 \log (x)+c_1}} \\ y(x)\to -((x-1) x) \\ \end{align*}