ODE
\[ \left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.186462 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {c_1}{a-x}\right \},\left \{y(x)\to \frac {c_1}{a+x}\right \}\right \}\]
Maple ✓
cpu = 0.046 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{a -x}, y \left (x \right ) = \frac {\textit {\_C1}}{a +x}\right ]\] Mathematica raw input
DSolve[-y[x]^2 - 2*x*y[x]*y'[x] + (a^2 - x^2)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/(a - x)}, {y[x] -> C[1]/(a + x)}}
Maple raw input
dsolve((a^2-x^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-y(x)^2 = 0, y(x))
Maple raw output
[y(x) = _C1/(a-x), y(x) = _C1/(a+x)]