Internal problem ID [8559]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 979.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 49
dsolve(diff(y(x),x) = (y(x)^3-3*x*y(x)^2+3*x^2*y(x)-x^3+x)/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {c_{1}-2 \ln \relax (x )}\, x -1}{\sqrt {c_{1}-2 \ln \relax (x )}} \\ y \relax (x ) = \frac {\sqrt {c_{1}-2 \ln \relax (x )}\, x +1}{\sqrt {c_{1}-2 \ln \relax (x )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.22 (sec). Leaf size: 42
DSolve[y'[x] == (x - x^3 + 3*x^2*y[x] - 3*x*y[x]^2 + y[x]^3)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\frac {1}{\sqrt {-2 \log (x)+c_1}} \\ y(x)\to x+\frac {1}{\sqrt {-2 \log (x)+c_1}} \\ y(x)\to x \\ \end{align*}