2.526   ODE No. 526

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

✓ Mathematica : cpu = 0.0504069 (sec), leaf count = 45

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

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

✓ Maple : cpu = 0.016 (sec), leaf count = 32

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

\[y \left (x \right ) = \frac {x^{3}}{3}+c_{1}\]