Internal problem ID [8066]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 486.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}+y^{2}-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 59
dsolve(y(x)^2*diff(y(x),x)^2+y(x)^2-a^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -a \\ y \relax (x ) = a \\ y \relax (x ) = \sqrt {a^{2}-x^{2}+2 x c_{1}-c_{1}^{2}} \\ y \relax (x ) = -\sqrt {a^{2}-x^{2}+2 x c_{1}-c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 101
DSolve[-a^2 + y[x]^2 + y[x]^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {a^2-(x+c_1){}^2} \\ y(x)\to \sqrt {a^2-(x+c_1){}^2} \\ y(x)\to -\sqrt {a^2-(x-c_1){}^2} \\ y(x)\to \sqrt {a^2-(x-c_1){}^2} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}