ODE No. 1728

$$a+2y(x)y^{″}(x)-y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0047571 (sec), leaf count = 31

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

$$\left\{\{y(x)\to \frac{x^2(-a+c_1{}^2)}{4c_2}+c_{1}x+c_2\}\right\}$$ ✓ Maple : cpu = 0.91 (sec), leaf count = 24

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

$$y\left(x\right)=\frac{(c_1^2-a)x^2}{4c_2}+c_{1}x+c_2$$