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]