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]