Internal problem ID [3648]
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]
\[ \boxed {\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {c_{1}}{-x +a} \\ y \left (x \right ) = \frac {c_{1}}{x +a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.049 (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*}