Internal problem ID [4155]
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]
\[ \boxed {\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 52
dsolve((a^2-x^2)*diff(y(x),x)^2 = x^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (a -x \right ) \left (x +a \right )}{\sqrt {a^{2}-x^{2}}}+c_{1} \\ y \left (x \right ) &= \frac {\left (a -x \right ) \left (x +a \right )}{\sqrt {a^{2}-x^{2}}}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (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^2-x^2}+c_1 \\ y(x)\to \sqrt {a^2-x^2}+c_1 \\ \end{align*}