ODE
\[ x^n f\left (y'(x),\frac {y(x)}{x}\right )=0 \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\)
Mathematica ✓
cpu = 0.877079 (sec), leaf count = 34
\[\text {Solve}\left [c_1=\int _1^{\frac {y(x)}{x}} \frac {1}{K[1]-\text {InverseFunction}[f,1,2][0,K[1]]} \, dK[1]+\log (x),y(x)\right ]\]
Maple ✓
cpu = 0.033 (sec), leaf count = 30
\[ \left \{ \ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\! \left ( {\it RootOf} \left ( f \left ( {\it \_Z},{\it \_a} \right ) \right ) -{\it \_a} \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x^n*f[y'[x], y[x]/x] == 0,y[x],x]
Mathematica raw output
Solve[C[1] == Integrate[(K[1] - InverseFunction[f, 1, 2][0, K[1]])^(-1), {K[1], 1, y[x]/x}] + Log[x], y[x]]
Maple raw input
dsolve(x^n*f(diff(y(x),x),y(x)/x) = 0, y(x),'implicit')
Maple raw output
ln(x)-Intat(1/(RootOf(f(_Z,_a))-_a),_a = y(x)/x)-_C1 = 0