ODE
\[ x^3 y(x) y'''(x)+3 x^3 y'(x) y''(x)+9 x^2 y(x) y''(x)+9 x^2 y'(x)^2+18 x y(x) y'(x)+3 y(x)^2=0 \] ODE Classification
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.23246 (sec), leaf count = 60
\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1 x^2+c_3 x+2 c_2}}{x^{3/2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1 x^2+c_3 x+2 c_2}}{x^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.128 (sec), leaf count = 24
\[ \left \{ {\frac {{\it \_C1}\,x}{2}}+{\frac {{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}{2}}+{\it \_C3}-{\frac {{\it \_C2}}{x}}=0 \right \} \] Mathematica raw input
DSolve[3*y[x]^2 + 18*x*y[x]*y'[x] + 9*x^2*y'[x]^2 + 9*x^2*y[x]*y''[x] + 3*x^3*y'[x]*y''[x] + x^3*y[x]*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[x^2*C[1] + 2*C[2] + x*C[3]]/x^(3/2))}, {y[x] -> Sqrt[x^2*C[1] + 2*C[2] + x*C[3]]/x^(3/2)}}
Maple raw input
dsolve(x^3*y(x)*diff(diff(diff(y(x),x),x),x)+3*x^3*diff(y(x),x)*diff(diff(y(x),x),x)+9*x^2*y(x)*diff(diff(y(x),x),x)+9*x^2*diff(y(x),x)^2+18*x*y(x)*diff(y(x),x)+3*y(x)^2 = 0, y(x),'implicit')
Maple raw output
1/2*_C1*x+1/2*x^2*y(x)^2+_C3-1/x*_C2 = 0