ODE
\[ 9 y(x)^2 y'''(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.268 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {1}{(x (c_3 x+c_2)+c_1){}^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 5.266 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C3}}{\left (\textit {\_C1} \,\textit {\_C2}^{2}+2 \textit {\_C1} x \textit {\_C2} +x^{2} \textit {\_C1} -9\right )^{\frac {3}{2}}}\right ]\] Mathematica raw input
DSolve[40*y'[x]^3 - 45*y[x]*y'[x]*y''[x] + 9*y[x]^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*(C[2] + x*C[3]))^(-3/2)}}
Maple raw input
dsolve(9*y(x)^2*diff(diff(diff(y(x),x),x),x)-45*y(x)*diff(y(x),x)*diff(diff(y(x),x),x)+40*diff(y(x),x)^3 = 0, y(x))
Maple raw output
[y(x) = 1/(_C1*_C2^2+2*_C1*_C2*x+_C1*x^2-9)^(3/2)*_C3]