2.1689   ODE No. 1689

\[ x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0 \]

✓ Mathematica : cpu = 0.300892 (sec), leaf count = 104

DSolve[(-y[x] + x*Derivative[1][y][x])^3 + x^4*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -i x \log \left (\frac {\frac {e^{c_2}}{x}-\frac {\sqrt {e^{2 c_2}-8 i c_1 x^2}}{x}}{4 c_1}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\frac {\sqrt {e^{2 c_2}-8 i c_1 x^2}}{x}+\frac {e^{c_2}}{x}}{4 c_1}\right )\right \}\right \}\]

✓ Maple : cpu = 0.126 (sec), leaf count = 37

dsolve(x^4*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^3=0,y(x))
 

\[y \left (x \right ) = \left (-\arctan \left (\frac {1}{\sqrt {c_{1} x^{2}-1}}\right )+c_{2} \right ) x\]