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 = 0.0706203 (sec), leaf count = 0 , could not solve
DSolve[40*Derivative[1][y][x]^3 - 45*y[x]*Derivative[1][y][x]*Derivative[2][y][x] + 9*y[x]^2*Derivative[3][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.302 (sec), leaf count = 22
\[ \left \{ \ln \left ( y \left ( x \right ) \right ) +{\frac {3\,\ln \left ( -9+ \left ( x+{\it \_C2} \right ) ^{2}{\it \_C1} \right ) }{2}}-{\it \_C3}=0 \right \} \] 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
DSolve[40*Derivative[1][y][x]^3 - 45*y[x]*Derivative[1][y][x]*Derivative[2][y][x] + 9*y[x]^2*Derivative[3][y][x] == 0, y[x], x]
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),'implicit')
Maple raw output
ln(y(x))+3/2*ln(-9+(x+_C2)^2*_C1)-_C3 = 0