ODE No. 417

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

✓ Mathematica : cpu = 0.0058208 (sec), leaf count = 16

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

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

✓ Maple : cpu = 0.03 (sec), leaf count = 35

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

\[y \left (x \right ) = -2 \sqrt {a x}\]