ODE
\[ x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.188063 (sec), leaf count = 49
\[\left \{\left \{y(x)\to -\sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )}\right \},\left \{y(x)\to \sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )}\right \}\right \}\]
Maple ✗
cpu = 1.667 (sec), leaf count = 0 , could not solve
dsolve(x*y(x)^2*diff(y(x),x)^3-y(x)^3*diff(y(x),x)^2+x*(x^2+1)*diff(y(x),x)-x^2*y(x) = 0, y(x))
Mathematica raw input
DSolve[-(x^2*y[x]) + x*(1 + x^2)*y'[x] - y[x]^3*y'[x]^2 + x*y[x]^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[C[1]*(x^2 + (1 + C[1]^2)^(-1))]}, {y[x] -> Sqrt[C[1]*(x^2 + (1 + C[1]^2)^(-1))]}}
Maple raw input
dsolve(x*y(x)^2*diff(y(x),x)^3-y(x)^3*diff(y(x),x)^2+x*(x^2+1)*diff(y(x),x)-x^2*y(x) = 0, y(x))
Maple raw output
dsolve(x*y(x)^2*diff(y(x),x)^3-y(x)^3*diff(y(x),x)^2+x*(x^2+1)*diff(y(x),x)-x^2*y(x) = 0, y(x))