2.439   ODE No. 439

\[ x^2 y'(x)^2+3 x y(x) y'(x)+3 y(x)^2=0 \]

✓ Mathematica : cpu = 0.0513123 (sec), leaf count = 49

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

\[\left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (-3-i \sqrt {3}\right )}\right \},\left \{y(x)\to c_1 x^{\frac {1}{2} i \left (\sqrt {3}+3 i\right )}\right \}\right \}\]

✓ Maple : cpu = 0.062 (sec), leaf count = 33

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

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