##### 4.9.27 $$y(x) y'(x)=a x+b y(x)^2$$

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

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.269134 (sec), leaf count = 77

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

Maple
cpu = 0.031 (sec), leaf count = 61

$\left [y \left (x \right ) = -\frac {\sqrt {4 \,{\mathrm e}^{2 b x} \textit {\_C1} \,b^{2}-4 a b x -2 a}}{2 b}, y \left (x \right ) = \frac {\sqrt {4 \,{\mathrm e}^{2 b x} \textit {\_C1} \,b^{2}-4 a b x -2 a}}{2 b}\right ]$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = -1/2*(4*exp(2*b*x)*_C1*b^2-4*a*b*x-2*a)^(1/2)/b, y(x) = 1/2*(4*exp(2*b*x
)*_C1*b^2-4*a*b*x-2*a)^(1/2)/b]