ODE No. 39

\[ -\text {a0}-\text {a1} y(x)-\text {a2} y(x)^2-\text {a3} y(x)^3+y'(x)=0 \] Mathematica : cpu = 0.138756 (sec), leaf count = 54

DSolve[-a0 - a1*y[x] - a2*y[x]^2 - a3*y[x]^3 + Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\& ,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\& \right ]=x+c_1,y(x)\right ]\] Maple : cpu = 0.016 (sec), leaf count = 30

dsolve(diff(y(x),x)-a3*y(x)^3-a2*y(x)^2-a1*y(x)-a0 = 0,y(x))
 

\[x -\left (\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{3} \mathit {a3} +\textit {\_a}^{2} \mathit {a2} +\textit {\_a} \mathit {a1} +\mathit {a0}}d \textit {\_a} \right )+c_{1} = 0\]