##### 4.9.30 $$y(x) y'(x)=a x+b x y(x)^2$$

ODE
$y(x) y'(x)=a x+b x y(x)^2$ ODE Classiﬁcation

[_separable]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.24705 (sec), leaf count = 62

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

Maple
cpu = 0.028 (sec), leaf count = 50

$\left [y \left (x \right ) = \frac {\sqrt {b \left ({\mathrm e}^{b \,x^{2}} \textit {\_C1} b -a \right )}}{b}, y \left (x \right ) = -\frac {\sqrt {b \left ({\mathrm e}^{b \,x^{2}} \textit {\_C1} b -a \right )}}{b}\right ]$ Mathematica raw input

DSolve[y[x]*y'[x] == a*x + b*x*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[-a + E^(b*(x^2 + 2*C[1]))]/Sqrt[b])}, {y[x] -> Sqrt[-a + E^(b*(
x^2 + 2*C[1]))]/Sqrt[b]}}

Maple raw input

dsolve(y(x)*diff(y(x),x) = a*x+b*x*y(x)^2, y(x))

Maple raw output

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