Internal problem ID [3444]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 706.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (x^{2}-y^{4}\right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 97
dsolve((x^2-y(x)^4)*diff(y(x),x) = x*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {2 c_{1}-2 \sqrt {-4 x^{2}+c_{1}^{2}}}}{2} \\ y \relax (x ) = \frac {\sqrt {2 c_{1}-2 \sqrt {-4 x^{2}+c_{1}^{2}}}}{2} \\ y \relax (x ) = -\frac {\sqrt {2 c_{1}+2 \sqrt {-4 x^{2}+c_{1}^{2}}}}{2} \\ y \relax (x ) = \frac {\sqrt {2 c_{1}+2 \sqrt {-4 x^{2}+c_{1}^{2}}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.109 (sec). Leaf size: 122
DSolve[(x^2-y[x]^4)y'[x]==x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to -\sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to 0 \\ \end{align*}