##### 4.11.15 $$x y(x) y'(x)=a+b y(x)^2$$

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.266044 (sec), leaf count = 58

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

Maple
cpu = 0.038 (sec), leaf count = 48

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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