4.12.35 \(x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )\)

ODE
\[ x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right ) \] ODE Classification

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type``class C`], _dAlembert]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.0374147 (sec), leaf count = 42

\[\text {Solve}\left [2 \left (\log \left (\frac {y(x)^2}{x^2}+1\right )+\log (x)\right )+3 \tan ^{-1}\left (\frac {y(x)}{x}\right )=c_1+4 \log \left (\frac {y(x)}{x}\right ),y(x)\right ]\]

Maple
cpu = 0.019 (sec), leaf count = 44

\[ \left \{ -\ln \left ({\frac {{x}^{2}+ \left (y \relax (x ) \right ) ^{2}}{{x}^{2}}} \right ) -{\frac {3}{2}\arctan \left ({\frac {y \relax (x ) }{x}} \right ) }+2\,\ln \left ({\frac {y \relax (x ) }{x}} \right ) -\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^2*(4*x - 3*y[x])*y'[x] == y[x]*(6*x^2 - 3*x*y[x] + 2*y[x]^2),y[x],x]

Mathematica raw output

Solve[3*ArcTan[y[x]/x] + 2*(Log[x] + Log[1 + y[x]^2/x^2]) == C[1] + 4*Log[y[x]/x
], y[x]]

Maple raw input

dsolve(x^2*(4*x-3*y(x))*diff(y(x),x) = (6*x^2-3*x*y(x)+2*y(x)^2)*y(x), y(x),'implicit')

Maple raw output

-ln((x^2+y(x)^2)/x^2)-3/2*arctan(y(x)/x)+2*ln(y(x)/x)-ln(x)-_C1 = 0