Internal problem ID [8471]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 891.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{2} \left (-2 y+2 x^{2}+2 y x^{2}+y x^{4}\right )}{x^{3} \left (x^{2}-y+y x^{2}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(diff(y(x),x) = y(x)^2/x^3*(-2*y(x)+2*x^2+2*x^2*y(x)+y(x)*x^4)/(x^2-y(x)+x^2*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{\sqrt {c_{1}-2 \ln \relax (x )}\, x^{2}-x^{2}+1} \\ y \relax (x ) = -\frac {x^{2}}{\sqrt {c_{1}-2 \ln \relax (x )}\, x^{2}+x^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.109 (sec). Leaf size: 77
DSolve[y'[x] == (y[x]^2*(2*x^2 - 2*y[x] + 2*x^2*y[x] + x^4*y[x]))/(x^3*(x^2 - y[x] + x^2*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt {\frac {1}{x^5}} \sqrt {x^5 (-2 \log (x)+1+c_1)}+\frac {1}{x^2}-1} \\ y(x)\to \frac {1}{-\sqrt {\frac {1}{x^5}} \sqrt {x^5 (-2 \log (x)+1+c_1)}+\frac {1}{x^2}-1} \\ y(x)\to 0 \\ \end{align*}