2.1782   ODE No. 1782

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

✓ Mathematica : cpu = 0.202986 (sec), leaf count = 93

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

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

✓ Maple : cpu = 0.067 (sec), leaf count = 33

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

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