##### 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 = 0.432276 (sec), leaf count = 42

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

Maple
cpu = 0.066 (sec), leaf count = 44

$\left [2 \ln \left (\frac {y \left (x \right )}{x}\right )-\ln \left (\frac {x^{2}+y \left (x \right )^{2}}{x^{2}}\right )-\frac {3 \arctan \left (\frac {y \left (x \right )}{x}\right )}{2}-\ln \left (x \right )-\textit {\_C1} = 0\right ]$ 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))

Maple raw output

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