Internal problem ID [3647]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 919.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (a^{2}-x^{2}\right ) \left (y^{\prime }\right )^{2}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.097 (sec). Leaf size: 52
dsolve((a^2-x^2)*diff(y(x),x)^2 = x^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (-x +a \right ) \left (a +x \right )}{\sqrt {\left (-x +a \right ) \left (a +x \right )}}+c_{1} \\ y \relax (x ) = \frac {\left (-x +a \right ) \left (a +x \right )}{\sqrt {\left (-x +a \right ) \left (a +x \right )}}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 43
DSolve[(a^2-x^2) (y'[x])^2==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {(a-x) (a+x)}+c_1 \\ y(x)\to \sqrt {(a-x) (a+x)}+c_1 \\ \end{align*}