Internal problem ID [15075]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 187.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (y^{2}-a^{2}+x^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 129
dsolve(( y(x)*(x^2+y(x)^2+a^2))*diff(y(x),x)+x*(x^2+y(x)^2-a^2)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-a^{2}-x^{2}-2 \sqrt {a^{2} x^{2}-c_{1}}} \\ y \left (x \right ) &= \sqrt {-a^{2}-x^{2}+2 \sqrt {a^{2} x^{2}-c_{1}}} \\ y \left (x \right ) &= -\sqrt {-a^{2}-x^{2}-2 \sqrt {a^{2} x^{2}-c_{1}}} \\ y \left (x \right ) &= -\sqrt {-a^{2}-x^{2}+2 \sqrt {a^{2} x^{2}-c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.374 (sec). Leaf size: 165
DSolve[( y[x]*(x^2+y[x]^2+a^2))*y'[x]+x*(x^2+y[x]^2-a^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-a^2-\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to \sqrt {-a^2-\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to -\sqrt {-a^2+\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to \sqrt {-a^2+\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ \end{align*}