ODE
\[ 8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.207319 (sec), leaf count = 49
\[\left \{\left \{y(x)\to -\frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}}\right \},\left \{y(x)\to \frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.102 (sec), leaf count = 80
\[\left [y \left (x \right ) = -\frac {3 x}{2}, y \left (x \right ) = \frac {3 x}{2}, y \left (x \right ) = 0, y \left (x \right ) = \frac {\left (\textit {\_C1} \left (3 \textit {\_C1} +x \right )\right )^{\frac {3}{2}} x}{\textit {\_C1}^{3} \left (-\frac {3 \left (3 \textit {\_C1} +x \right )}{\textit {\_C1}}+9\right )}, y \left (x \right ) = -\frac {\left (\textit {\_C1} \left (3 \textit {\_C1} +x \right )\right )^{\frac {3}{2}} x}{\textit {\_C1}^{3} \left (-\frac {3 \left (3 \textit {\_C1} +x \right )}{\textit {\_C1}}+9\right )}\right ]\] Mathematica raw input
DSolve[9*y[x] - 12*y[x]*y'[x]^2 + 8*x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/3*(x + 3*C[1])^(3/2)/Sqrt[C[1]]}, {y[x] -> (x + 3*C[1])^(3/2)/(3*Sqrt[C[1]])}}
Maple raw input
dsolve(8*x*diff(y(x),x)^3-12*y(x)*diff(y(x),x)^2+9*y(x) = 0, y(x))
Maple raw output
[y(x) = -3/2*x, y(x) = 3/2*x, y(x) = 0, y(x) = 1/_C1^3*(_C1*(3*_C1+x))^(3/2)*x/(-3/_C1*(3*_C1+x)+9), y(x) = -1/_C1^3*(_C1*(3*_C1+x))^(3/2)*x/(-3/_C1*(3*_C1+x)+9)]