2.415   ODE No. 415

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

✓ Mathematica : cpu = 0.234241 (sec), leaf count = 49

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

\[\left \{\left \{y(x)\to -\frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}}\right \},\left \{y(x)\to \frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}}\right \}\right \}\]

✓ Maple : cpu = 0.261 (sec), leaf count = 95

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

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