Internal problem ID [3649]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 921.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (a^{2}-x^{2}\right ) \left (y^{\prime }\right )^{2}-2 y^{\prime } y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 23
dsolve((a^2-x^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1}}{-x +a} \\ y \relax (x ) = \frac {c_{1}}{a +x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 32
DSolve[(a^2-x^2) (y'[x])^2-2 x y[x] y'[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{a-x} \\ y(x)\to \frac {c_1}{a+x} \\ y(x)\to 0 \\ \end{align*}