2.455   ODE No. 455

\[ a+x^3 y'(x)^2+x^2 y(x) y'(x)=0 \] Mathematica : cpu = 0.402527 (sec), leaf count = 57

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

\[\left \{\left \{y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x}\right \},\left \{y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x}\right \}\right \}\] Maple : cpu = 0.294 (sec), leaf count = 66

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

\[y \left (x \right ) = -\frac {2 \sqrt {a x}}{x}\]