Internal problem ID [8554]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 974.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-y^{3}+3 y^{2} x^{2}-3 y x^{4}+x^{6}-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve(diff(y(x),x) = y(x)^3-3*x^2*y(x)^2+3*y(x)*x^4-x^6+2*x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2} \sqrt {2 c_{1}-2 x}-1}{\sqrt {2 c_{1}-2 x}} \\ y \relax (x ) = \frac {x^{2} \sqrt {2 c_{1}-2 x}+1}{\sqrt {2 c_{1}-2 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 46
DSolve[y'[x] == 2*x - x^6 + 3*x^4*y[x] - 3*x^2*y[x]^2 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to x^2+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to x^2 \\ \end{align*}