ODE No. 1829

\[ 3 x^2 y''(x)^2+4 y'(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)=0 \]

✓ Mathematica : cpu = 0.0067519 (sec), leaf count = 24

DSolve[4*Derivative[1][y][x]^2 - 2*(y[x] + 3*x*Derivative[1][y][x])*Derivative[2][y][x] + 3*x^2*Derivative[2][y][x]^2 == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {c_1{}^2 x^2}{c_2}+c_1 x+c_2\right \}\right \}\]

✓ Maple : cpu = 0.661 (sec), leaf count = 36

dsolve(3*x^2*diff(diff(y(x),x),x)^2-2*(3*x*diff(y(x),x)+y(x))*diff(diff(y(x),x),x)+4*diff(y(x),x)^2=0,y(x))

\[y \left (x \right ) = x^{\frac {2 \sqrt {3}}{3}} c_{1} x\]