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

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

[_rational]

Book solution method
Change of variable

Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out

$Aborted

Maple ✗
cpu = 0.01 (sec), leaf count = 0 , exception

time expired

Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

time expired