Internal problem ID [3419]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 680.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\left (a +x^{2}+y^{2}\right ) y y^{\prime }-x \left (a -x^{2}-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 113
dsolve((a+x^2+y(x)^2)*y(x)*diff(y(x),x) = x*(a-x^2-y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x^{2}-a -2 \sqrt {a \,x^{2}-c_{1}}} \\ y \relax (x ) = \sqrt {-x^{2}-a +2 \sqrt {a \,x^{2}-c_{1}}} \\ y \relax (x ) = -\sqrt {-x^{2}-a -2 \sqrt {a \,x^{2}-c_{1}}} \\ y \relax (x ) = -\sqrt {-x^{2}-a +2 \sqrt {a \,x^{2}-c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 8.562 (sec). Leaf size: 149
DSolve[(a+x^2+y[x]^2)y[x] y'[x]==x(a-x^2-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2} \\ y(x)\to \sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2} \\ y(x)\to -\sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2} \\ y(x)\to \sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2} \\ \end{align*}