ODE
\[ 4 y(x)^2 y'''(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.269302 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \frac {1}{(x (c_3 x+c_2)+c_1){}^2}\right \}\right \}\]
Maple ✓
cpu = 4.755 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C3}}{\left (\textit {\_C1} \,\textit {\_C2}^{2}+2 \textit {\_C1} x \textit {\_C2} +x^{2} \textit {\_C1} -4\right )^{2}}\right ]\] Mathematica raw input
DSolve[15*y'[x]^3 - 18*y[x]*y'[x]*y''[x] + 4*y[x]^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*(C[2] + x*C[3]))^(-2)}}
Maple raw input
dsolve(4*y(x)^2*diff(diff(diff(y(x),x),x),x)-18*y(x)*diff(y(x),x)*diff(diff(y(x),x),x)+15*diff(y(x),x)^3 = 0, y(x))
Maple raw output
[y(x) = _C3/(_C1*_C2^2+2*_C1*_C2*x+_C1*x^2-4)^2]