4.19.26 $(a^2+x^2)y^{\prime }(x{)}^2+b-2xy(x)y^{\prime }(x)+y(x{)}^2=0$

ODE
$$(a^2+x^2)y^{\prime }(x{)}^2+b-2xy(x)y^{\prime }(x)+y(x{)}^2=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Book solution method
Clairaut’s equation and related types, $f(y-x{y}^{\prime },y^{\prime })=0$

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

$Aborted

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

$$\{\frac{a^2{\left(y\left(x\right)\right)}^2+b(a^2+x^2)}{a^2}=0,y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x-\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-b},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-b}\}$$ 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)