ODE
\[ (a-x) y'(x)=y(x)^3 (b+c x)+y(x) \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0185469 (sec), leaf count = 77
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {a^2 c_1+a \left (c-2 c_1 x\right )-b+x \left (c_1 x-2 c\right )}}\right \},\left \{y(x)\to \frac {1}{\sqrt {a^2 c_1+a \left (c-2 c_1 x\right )-b+x \left (c_1 x-2 c\right )}}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 35
\[ \left \{ {\frac {1+ \left ( - \left ( a-x \right ) ^{2}{\it \_C1}-ca+2\,cx+b \right ) \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}}=0 \right \} \] Mathematica raw input
DSolve[(a - x)*y'[x] == y[x] + (b + c*x)*y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> -(1/Sqrt[-b + a^2*C[1] + a*(c - 2*x*C[1]) + x*(-2*c + x*C[1])])}, {y[x] -> 1/Sqrt[-b + a^2*C[1] + a*(c - 2*x*C[1]) + x*(-2*c + x*C[1])]}}
Maple raw input
dsolve((a-x)*diff(y(x),x) = y(x)+(c*x+b)*y(x)^3, y(x),'implicit')
Maple raw output
(1+(-(a-x)^2*_C1-c*a+2*c*x+b)*y(x)^2)/y(x)^2 = 0