Internal problem ID [4083]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 844.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}=-x^{2}+a} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 46
dsolve(x*diff(y(x),x)^2 = -x^2+a,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \int \frac {\sqrt {x \left (-x^{2}+a \right )}}{x}d x +c_{1} y \left (x \right ) = \int -\frac {\sqrt {x \left (-x^{2}+a \right )}}{x}d x +c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 5.7 (sec). Leaf size: 113
DSolve[x (y'[x])^2==(a-x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 \sqrt {x} \sqrt {a-x^2} \operatorname {Hypergeometric2F1}\left (-\frac {1}{2},\frac {1}{4},\frac {5}{4},\frac {x^2}{a}\right )}{\sqrt {1-\frac {x^2}{a}}}+c_1 y(x)\to \frac {2 \sqrt {x} \sqrt {a-x^2} \operatorname {Hypergeometric2F1}\left (-\frac {1}{2},\frac {1}{4},\frac {5}{4},\frac {x^2}{a}\right )}{\sqrt {1-\frac {x^2}{a}}}+c_1 \end{align*}