ODE
\[ x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.20814 (sec), leaf count = 50
\[\left \{\left \{y(x)\to -\frac {4 e^{2 c_1} x}{2 e^{c_1}-x}\right \},\left \{y(x)\to \frac {e^{2 c_1} x}{2 e^{c_1}+4 x}\right \}\right \}\]
Maple ✓
cpu = 0.177 (sec), leaf count = 84
\[ \left \{ 2\, \left ( y \left ( x \right ) \right ) ^{-1}+{x}^{-2}+{\frac {1}{{x}^{2}y \left ( x \right ) }\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+4\,{x}^{2}y \left ( x \right ) }}-{\it \_C1}=0,2\,y \left ( x \right ) +{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}+{\frac {y \left ( x \right ) }{{x}^{2}}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+4\,{x}^{2}y \left ( x \right ) }}-{\it \_C1}=0,y \left ( x \right ) =-4\,{x}^{2} \right \} \] Mathematica raw input
DSolve[-y[x]^3 + x*y[x]^2*y'[x] + x^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-4*E^(2*C[1])*x)/(2*E^C[1] - x)}, {y[x] -> (E^(2*C[1])*x)/(2*E^C[1] + 4*x)}}
Maple raw input
dsolve(x^4*diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)-y(x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = -4*x^2, 2*y(x)+y(x)^2/x^2+y(x)/x^2*(y(x)^2+4*x^2*y(x))^(1/2)-_C1 = 0, 2/y(x)+1/x^2+1/y(x)/x^2*(y(x)^2+4*x^2*y(x))^(1/2)-_C1 = 0