4.19.26 \(\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0\)

ODE
\[ \left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Book solution method
Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Mathematica
cpu = 601.717 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.044 (sec), leaf count = 69

\[ \left \{ {\frac {{a}^{2} \left (y \relax (x ) \right ) ^{2}+b \left ({a}^{2}+{x}^{2} \right ) }{{a}^{2}}}=0,y \relax (x ) ={\it \_C1}\,x-\sqrt {-{{\it \_C1}}^{2}{a}^{2}-b},y \relax (x ) ={\it \_C1}\,x+\sqrt {-{{\it \_C1}}^{2}{a}^{2}-b} \right \} \] Mathematica raw input

DSolve[b + y[x]^2 - 2*x*y[x]*y'[x] + (a^2 + x^2)*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve((a^2+x^2)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+b+y(x)^2 = 0, y(x),'implicit')

Maple raw output

(a^2*y(x)^2+b*(a^2+x^2))/a^2 = 0, y(x) = _C1*x-(-_C1^2*a^2-b)^(1/2), y(x) = _C1*
x+(-_C1^2*a^2-b)^(1/2)