4.5.38 \((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\)

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

\[ \left \{ {\frac {1+ \left (- \left (a-x \right ) ^{2}{\it \_C1}-ca+2\,cx+b \right ) \left (y \relax (x ) \right ) ^{2}}{ \left (y \relax (x ) \right ) ^{2}}}=0 \right \} \] 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