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 = 0.192186 (sec), leaf count = 24

\[\left \{\left \{y(x)\to \sqrt {c_1 \left (x^2+\frac {a}{1+c_1}\right )}\right \}\right \}\]

Maple ✗
cpu = 0. (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

{{y[x] -> Sqrt[C[1]*(x^2 + a/(1 + C[1]))]}}

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))

Maple raw output

\verbtime expired||