2.1800   ODE No. 1800

\[ y(x) \left (y(x)^2+1\right ) y''(x)+\left (1-3 y(x)^2\right ) y'(x)^2=0 \]

✓ Mathematica : cpu = 0.542209 (sec), leaf count = 84

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {-2 c_1 x-1-2 c_2 c_1}}{\sqrt {2} \sqrt {c_1 x+c_2 c_1}}\right \},\left \{y(x)\to \frac {\sqrt {-2 c_1 x-1-2 c_2 c_1}}{\sqrt {2} \sqrt {c_1 x+c_2 c_1}}\right \}\right \}\]

✓ Maple : cpu = 0.06 (sec), leaf count = 60

dsolve(y(x)*(y(x)^2+1)*diff(diff(y(x),x),x)+(1-3*y(x)^2)*diff(y(x),x)^2=0,y(x))
 

\[y \left (x \right ) = -\frac {\sqrt {-4 \left (x c_{1} +c_{2} +\frac {1}{2}\right ) \left (x c_{1} +c_{2} \right )}}{2 x c_{1} +2 c_{2}}\]