4.11.36 \(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\)

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 = 0.037646 (sec), leaf count = 90

\[\left \{\left \{y(x)\to -\frac {e^{\frac {c_1}{2}} \sqrt {e^{c_1}+12 x^2}+e^{c_1}+4 x^2}{2 x}\right \},\left \{y(x)\to -\frac {-e^{\frac {c_1}{2}} \sqrt {e^{c_1}+12 x^2}+e^{c_1}+4 x^2}{2 x}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 37

\[ \left \{ -\ln \left ({\frac {2\,x+y \relax (x ) }{x}} \right ) +{\frac {1}{2}\ln \left ({\frac {y \relax (x ) -x}{x}} \right ) }-\ln \relax (x ) -{\it \_C1}=0 \right \} \] 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] -> -(E^C[1] + 4*x^2 + E^(C[1]/2)*Sqrt[E^C[1] + 12*x^2])/(2*x)}, {y[x] -> 
-(E^C[1] + 4*x^2 - E^(C[1]/2)*Sqrt[E^C[1] + 12*x^2])/(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),'implicit')

Maple raw output

-ln((2*x+y(x))/x)+1/2*ln((y(x)-x)/x)-ln(x)-_C1 = 0