ODE No. 1715

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

✓ Mathematica : cpu = 0.128384 (sec), leaf count = 26

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

\[\left \{\left \{y(x)\to c_2 (-a x+x-c_1){}^{\frac {1}{1-a}}\right \}\right \}\]

✓ Maple : cpu = 0.067 (sec), leaf count = 25

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

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