Internal problem ID [8320]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 740.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 72
dsolve(diff(y(x),x) = (x+y(x)^4-2*x^2*y(x)^2+x^4)/y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {2}\, \sqrt {\left (c_{1}+x \right ) \left (2 c_{1} x^{2}+2 x^{3}-1\right )}}{2 x +2 c_{1}} \\ y \relax (x ) = \frac {\sqrt {2}\, \sqrt {\left (c_{1}+x \right ) \left (2 c_{1} x^{2}+2 x^{3}-1\right )}}{2 x +2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.639 (sec). Leaf size: 126
DSolve[y'[x] == (x + x^4 - 2*x^2*y[x]^2 + y[x]^4)/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-1+2 x^2 (x+c_1)}}{\sqrt {2} \sqrt {x+c_1}} \\ y(x)\to \frac {\sqrt {-1+2 x^2 (x+c_1)}}{\sqrt {2} \sqrt {x+c_1}} \\ y(x)\to -i \sqrt {-x^2} \\ y(x)\to i \sqrt {-x^2} \\ y(x)\to -\sqrt {x^2} \\ y(x)\to \sqrt {x^2} \\ \end{align*}