ODE No. 1683

\[ x^3 y''(x)-a \left (x y'(x)-y(x)\right )^2=0 \]

✓ Mathematica : cpu = 0.0881766 (sec), leaf count = 26

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

\[\left \{\left \{y(x)\to -\frac {x \log \left (a \left (-\frac {c_1}{x}-c_2\right )\right )}{a}\right \}\right \}\]

✓ Maple : cpu = 0.062 (sec), leaf count = 23

dsolve(x^3*diff(diff(y(x),x),x)-a*(x*diff(y(x),x)-y(x))^2=0,y(x))

\[y \left (x \right ) = -\frac {\ln \left (\frac {a \left (x c_{1} -c_{2} \right )}{x}\right ) x}{a}\]