ODE
\[ 3 y(x)^2 y'(x)=a y(x)^3+x+1 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0378441 (sec), leaf count = 111
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{a^2 c_1 e^{a x}-a (x+1)-1}}{a^{2/3}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{a^2 c_1 e^{a x}-a (x+1)-1}}{a^{2/3}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{a^2 c_1 e^{a x}-a (x+1)-1}}{a^{2/3}}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 26
\[ \left \{ {\frac {x}{a}}+{a}^{-1}+{a}^{-2}-{{\rm e}^{ax}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{3}=0 \right \} \] Mathematica raw input
DSolve[3*y[x]^2*y'[x] == 1 + x + a*y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> (-1 - a*(1 + x) + a^2*E^(a*x)*C[1])^(1/3)/a^(2/3)}, {y[x] -> -(((-1)^(1/3)*(-1 - a*(1 + x) + a^2*E^(a*x)*C[1])^(1/3))/a^(2/3))}, {y[x] -> ((-1)^(2/3)*(-1 - a*(1 + x) + a^2*E^(a*x)*C[1])^(1/3))/a^(2/3)}}
Maple raw input
dsolve(3*y(x)^2*diff(y(x),x) = 1+x+a*y(x)^3, y(x),'implicit')
Maple raw output
1/a*x+1/a+1/a^2-exp(a*x)*_C1+y(x)^3 = 0