\[ x^4 y''(x)-x \left (x^2+2 y(x)\right ) y'(x)+4 y(x)^2=0 \] ✓ Mathematica : cpu = 0.0715044 (sec), leaf count = 262
DSolve[4*y[x]^2 - x*(x^2 + 2*y[x])*Derivative[1][y][x] + x^4*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {x^3 \left (i \left (\frac {i}{\sqrt {c_1}}-\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}\right ) \sqrt {c_1} c_2 x^{-1+i \left (\frac {i}{\sqrt {c_1}}-\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}\right ) \sqrt {c_1}}+i \left (\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}+\frac {i}{\sqrt {c_1}}\right ) \sqrt {c_1} x^{-1+i \left (\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}+\frac {i}{\sqrt {c_1}}\right ) \sqrt {c_1}}\right )}{c_2 x^{i \left (\frac {i}{\sqrt {c_1}}-\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}\right ) \sqrt {c_1}}+x^{i \left (\frac {\sqrt {-1-c_1}}{\sqrt {c_1}}+\frac {i}{\sqrt {c_1}}\right ) \sqrt {c_1}}}\right \}\right \}\] ✓ Maple : cpu = 0.906 (sec), leaf count = 21
dsolve(x^4*diff(diff(y(x),x),x)-x*(x^2+2*y(x))*diff(y(x),x)+4*y(x)^2=0,y(x))
\[y \left (x \right ) = x^{2} \left (\tanh \left (c_{1} \left (c_{2}-\ln \left (x \right )\right )\right ) c_{1}+1\right )\]