ODE No. 457

\[ x^4 y'(x)^2-x y'(x)-y(x)=0 \] Mathematica : cpu = 0.378635 (sec), leaf count = 118

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

\[\left \{\text {Solve}\left [-\frac {x \sqrt {4 x^2 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ],\text {Solve}\left [\frac {x \sqrt {4 x^2 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 1.25 (sec), leaf count = 45

dsolve(x^4*diff(y(x),x)^2-x*diff(y(x),x)-y(x) = 0,y(x))
 

\[y \left (x \right ) = -\frac {1}{4 x^{2}}\]