##### 4.11.32 $$2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0$$

ODE
$2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0$ ODE Classiﬁcation

[[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.270267 (sec), leaf count = 54

$\left \{\left \{y(x)\to x-\frac {\sqrt {2 x^4+e^{2 c_1}}}{x}\right \},\left \{y(x)\to x+\frac {\sqrt {2 x^4+e^{2 c_1}}}{x}\right \}\right \}$

Maple
cpu = 0.2 (sec), leaf count = 59

$\left [y \left (x \right ) = \frac {x^{2} \textit {\_C1} -\sqrt {2 x^{4} \textit {\_C1}^{2}+1}}{\textit {\_C1} x}, y \left (x \right ) = \frac {x^{2} \textit {\_C1} +\sqrt {2 x^{4} \textit {\_C1}^{2}+1}}{\textit {\_C1} x}\right ]$ Mathematica raw input

DSolve[2*x^2 + 3*x*y[x] - y[x]^2 + x*(x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x - Sqrt[E^(2*C[1]) + 2*x^4]/x}, {y[x] -> x + Sqrt[E^(2*C[1]) + 2*x^4]
/x}}

Maple raw input

dsolve(x*(x-y(x))*diff(y(x),x)+2*x^2+3*x*y(x)-y(x)^2 = 0, y(x))

Maple raw output

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