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 = 387.175 (sec), leaf count = 0 , could not solve
DSolve[-(x^2*y[x]) + x*(1 + x^2)*Derivative[1][y][x] - y[x]^3*Derivative[1][y][x]^2 + x*y[x]^2*Derivative[1][y][x]^3 == 0, y[x], x]
Maple ✓
cpu = 1.536 (sec), leaf count = 37
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{8}+{\frac { \left ( 8\,{x}^{4}-20\,{x}^{2}-1 \right ) \left ( y \left ( x \right ) \right ) ^{4}}{4}}+{x}^{2} \left ( {x}^{2}+1 \right ) ^{3}=0 \right \} \] 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
DSolve[-(x^2*y[x]) + x*(1 + x^2)*Derivative[1][y][x] - y[x]^3*Derivative[1][y][x]^2 + x*y[x]^2*Derivative[1][y][x]^3 == 0, y[x], x]
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),'implicit')
Maple raw output
y(x)^8+1/4*(8*x^4-20*x^2-1)*y(x)^4+x^2*(x^2+1)^3 = 0