ODE
\[ \left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2=4 x y(x) \left (x y'(x)-y(x)\right )^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 16.1333 (sec), leaf count = 0 , could not solve
DSolve[(y[x]^2 - x^2*Derivative[1][y][x]^2 + x^2*y[x]*Derivative[2][y][x])^2 == 4*x*y[x]*(-y[x] + x*Derivative[1][y][x])^3, y[x], x]
Maple ✓
cpu = 0.466 (sec), leaf count = 82
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{{{\it \_a}}^{2}} \left ( 2\,\sqrt {{\it \_a}\, \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) -1 \right ) }{\it \_b} \left ( {\it \_a} \right ) {\it \_a}-2\,\sqrt {{\it \_a}\, \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) -1 \right ) }-1 \right ) } \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[(y[x]^2 - x^2*y'[x]^2 + x^2*y[x]*y''[x])^2 == 4*x*y[x]*(-y[x] + x*y'[x])^3,y[x],x]
Mathematica raw output
DSolve[(y[x]^2 - x^2*Derivative[1][y][x]^2 + x^2*y[x]*Derivative[2][y][x])^2 == 4*x*y[x]*(-y[x] + x*Derivative[1][y][x])^3, y[x], x]
Maple raw input
dsolve((y(x)^2-x^2*diff(y(x),x)^2+x^2*y(x)*diff(diff(y(x),x),x))^2 = 4*x*y(x)*(x*diff(y(x),x)-y(x))^3, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(exp(Int(_b(_a),_a)+_C1),[{diff(_b(_a),_a) = (2*(_a*(_a*_b(_a)-1))^(1/2)*_b(_a)*_a-2*(_a*(_a*_b(_a)-1))^(1/2)-1)/_a^2}, {_a = x, _b(_a) = diff(y(x),x)/y(x)}, {x = _a, y(x) = exp(Int(_b(_a),_a)+_C1)}])