4.12.35 $x^2(4x-3y(x))y^{\prime }(x)=y(x)(6x^2-3xy(x)+2y(x{)}^2)$

ODE
$$x^2(4x-3y(x))y^{\prime }(x)=y(x)(6x^2-3xy(x)+2y(x{)}^2)$$ 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

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

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

$$\{-\ln \left(\frac{x^2+{\left(y\left(x\right)\right)}^2}{x^2}\right)-\frac{3}{2}\arctan \left(\frac{y\left(x\right)}{x}\right)+2\ln \left(\frac{y\left(x\right)}{x}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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