ODE
\[ 4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.30422 (sec), leaf count = 90
\[\left \{\left \{y(x)\to -\frac {4 x^2+e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x}\right \},\left \{y(x)\to -\frac {4 x^2-e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.19 (sec), leaf count = 69
\[\left [y \left (x \right ) = \frac {-2 x \textit {\_C1} +\frac {1+\sqrt {-12 \textit {\_C1}^{2} x^{2}+1}}{2 x \textit {\_C1}}}{\textit {\_C1}}, y \left (x \right ) = \frac {-2 x \textit {\_C1} -\frac {-1+\sqrt {-12 \textit {\_C1}^{2} x^{2}+1}}{2 x \textit {\_C1}}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[4*x^2 - 6*x*y[x] - y[x]^2 + x*(4*x - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*(E^C[1] + 4*x^2 + E^(C[1]/2)*Sqrt[E^C[1] + 12*x^2])/x}, {y[x] -> -1/2*(E^C[1] + 4*x^2 - E^(C[1]/2)*Sqrt[E^C[1] + 12*x^2])/x}}
Maple raw input
dsolve(x*(4*x-y(x))*diff(y(x),x)+4*x^2-6*x*y(x)-y(x)^2 = 0, y(x))
Maple raw output
[y(x) = (-2*x*_C1+1/2/x/_C1*(1+(-12*_C1^2*x^2+1)^(1/2)))/_C1, y(x) = (-2*x*_C1-1/2*(-1+(-12*_C1^2*x^2+1)^(1/2))/x/_C1)/_C1]