4.19.25 \(\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0\)

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 = 0.00769023 (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 = 0.015 (sec), leaf count = 23

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{a-x}},y \relax (x ) ={\frac {{\it \_C1}}{a+x}} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1/(a-x), y(x) = _C1/(a+x)