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 = 0.02603 (sec), leaf count = 54
\[\left \{\left \{y(x)\to x-\frac {\sqrt {e^{2 c_1}+2 x^4}}{x}\right \},\left \{y(x)\to \frac {\sqrt {e^{2 c_1}+2 x^4}}{x}+x\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 33
\[ \left \{ -{\frac {1}{4}\ln \left ( {\frac {-{x}^{2}-2\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
-1/4*ln((-x^2-2*x*y(x)+y(x)^2)/x^2)-ln(x)-_C1 = 0