ODE
\[ x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.484177 (sec), leaf count = 95
\[\left \{\left \{y(x)\to -i x \log \left (\frac {e^{c_2}-\sqrt {e^{2 c_2}-8 i c_1 x^2}}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\sqrt {e^{2 c_2}-8 i c_1 x^2}+e^{c_2}}{4 c_1 x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.722 (sec), leaf count = 37
\[\left [y \left (x \right ) = \left (-\arctan \left (\frac {1}{\sqrt {x^{2} \textit {\_C1} -1}}\right )+\textit {\_C2} \right ) x, y \left (x \right ) = \left (\arctan \left (\frac {1}{\sqrt {x^{2} \textit {\_C1} -1}}\right )+\textit {\_C2} \right ) x\right ]\] Mathematica raw input
DSolve[(-y[x] + x*y'[x])^3 + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-I)*x*Log[(E^C[2] - Sqrt[E^(2*C[2]) - (8*I)*x^2*C[1]])/(4*x*C[1])]}, {y[x] -> (-I)*x*Log[(E^C[2] + Sqrt[E^(2*C[2]) - (8*I)*x^2*C[1]])/(4*x*C[1])]}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^3 = 0, y(x))
Maple raw output
[y(x) = (-arctan(1/(_C1*x^2-1)^(1/2))+_C2)*x, y(x) = (arctan(1/(_C1*x^2-1)^(1/2))+_C2)*x]