Internal problem ID [8643]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 307.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {\left (y^{2}+x^{2}+a \right ) y y^{\prime }+x \left (y^{2}+x^{2}-a \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 113
dsolve((y(x)^2+x^2+a)*y(x)*diff(y(x),x)+(y(x)^2+x^2-a)*x = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-x^{2}-a -2 \sqrt {a \,x^{2}-c_{1}}} \\ y \left (x \right ) &= \sqrt {-x^{2}-a +2 \sqrt {a \,x^{2}-c_{1}}} \\ y \left (x \right ) &= -\sqrt {-x^{2}-a -2 \sqrt {a \,x^{2}-c_{1}}} \\ y \left (x \right ) &= -\sqrt {-x^{2}-a +2 \sqrt {a \,x^{2}-c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 8.667 (sec). Leaf size: 149
DSolve[x*(-a + x^2 + y[x]^2) + y[x]*(a + x^2 + y[x]^2)*y'[x]==0,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*}