##### 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 = 0.336053 (sec), leaf count = 77

$\left \{\left \{y(x)\to -\frac {1}{\sqrt {a^2 c_1+a (c-2 c_1 x)-b+x (-2 c+c_1 x)}}\right \},\left \{y(x)\to \frac {1}{\sqrt {a^2 c_1+a (c-2 c_1 x)-b+x (-2 c+c_1 x)}}\right \}\right \}$

Maple
cpu = 0.023 (sec), leaf count = 65

$\left [y \left (x \right ) = \frac {1}{\sqrt {\textit {\_C1} \,a^{2}-2 \textit {\_C1} a x +x^{2} \textit {\_C1} +c a -2 c x -b}}, y \left (x \right ) = -\frac {1}{\sqrt {\textit {\_C1} \,a^{2}-2 \textit {\_C1} a x +x^{2} \textit {\_C1} +c a -2 c x -b}}\right ]$ 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))

Maple raw output

[y(x) = 1/(_C1*a^2-2*_C1*a*x+_C1*x^2+a*c-2*c*x-b)^(1/2), y(x) = -1/(_C1*a^2-2*_C
1*a*x+_C1*x^2+a*c-2*c*x-b)^(1/2)]