Internal problem ID [8329]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 749.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 186
dsolve(diff(y(x),x) = (x-y(x))^2*(x+y(x))^2*x/y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\ y \relax (x ) = -\frac {\sqrt {\left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 21.512 (sec). Leaf size: 102
DSolve[y'[x] == (x*(x - y[x])^2*(x + y[x])^2)/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+\left (x^2-1\right ) e^{2 x^2+4 c_1}+1}}{\sqrt {1+e^{2 x^2+4 c_1}}} \\ y(x)\to \frac {\sqrt {x^2+\left (x^2-1\right ) e^{2 x^2+4 c_1}+1}}{\sqrt {1+e^{2 x^2+4 c_1}}} \\ \end{align*}