ODE
\[ a y(x)^3+9 x^2 y''(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 3.24699 (sec), leaf count = 0 , could not solve
DSolve[2*y[x] + a*y[x]^3 + 9*x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.101 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{\it JacobiSN} \left ( \left ( {\frac {\sqrt {2}}{2\,{x}^{3}}\sqrt {{x}^{{\frac {20}{3}}}a}}+{\it \_C1} \right ) {\it \_C2},i \right ) \sqrt [3]{x} \right \} \] Mathematica raw input
DSolve[2*y[x] + a*y[x]^3 + 9*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[2*y[x] + a*y[x]^3 + 9*x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(9*x^2*diff(diff(y(x),x),x)+a*y(x)^3+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*JacobiSN((1/2/x^3*2^(1/2)*(x^(20/3)*a)^(1/2)+_C1)*_C2,I)*x^(1/3)