Internal problem ID [9075]
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]
\[ \boxed {y^{\prime }-\frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y}=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (c_{1} +x \right ) \left (2 x^{2} c_{1} +2 x^{3}-1\right )}}{2 c_{1} +2 x} y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {\left (c_{1} +x \right ) \left (2 x^{2} c_{1} +2 x^{3}-1\right )}}{2 c_{1} +2 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.661 (sec). Leaf size: 132
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 {2 x^3+2 c_1 x^2-1}}{\sqrt {2} \sqrt {x+c_1}} y(x)\to \frac {\sqrt {2 x^3+2 c_1 x^2-1}}{\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*}