[[_homogeneous, `class G`]]
Book solution method
No Missing Variables ODE, Solve for
Mathematica ✓
cpu = 0.415011 (sec), leaf count = 120
Maple ✓
cpu = 0.069 (sec), leaf count = 71
DSolve[9*y[x] + 3*x*y'[x] + x^8*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{Solve[6*C[1] + Log[y[x]] + (2*ArcTan[Sqrt[-1 + 4*x^6*y[x]]]*Sqrt[x^2 - 4*x^8*y[
x]])/(x*Sqrt[-1 + 4*x^6*y[x]]) == 0, y[x]], Solve[6*C[1] + Log[y[x]] == (2*ArcTa
n[Sqrt[-1 + 4*x^6*y[x]]]*Sqrt[x^2 - 4*x^8*y[x]])/(x*Sqrt[-1 + 4*x^6*y[x]]), y[x]
]}
Maple raw input
dsolve(x^8*diff(y(x),x)^2+3*x*diff(y(x),x)+9*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/4/x^6, ln(x)-_C1-1/6*ln(y(x)*x^6)+1/3*arctanh((1-4*y(x)*x^6)^(1/2)) = 0
, ln(x)-_C1-1/6*ln(y(x)*x^6)-1/3*arctanh((1-4*y(x)*x^6)^(1/2)) = 0