2.111   ODE No. 111

\[ x y'(x)+y(x)^3+3 x y(x)^2=0 \] Mathematica : cpu = 0.336056 (sec), leaf count = 55

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

\[\text {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ]\] Maple : cpu = 0.089 (sec), leaf count = 53

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

\[c_{1}-\frac {i {\mathrm e}^{\frac {\left (3 x y \left (x \right )-1\right )^{2}}{2 y \left (x \right )^{2}}}}{3 x}+\frac {\operatorname {erf}\left (\frac {i \left (3 x y \left (x \right )-1\right ) \sqrt {2}}{2 y \left (x \right )}\right ) \sqrt {2}\, \sqrt {\pi }}{2} = 0\]