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 = 2.66214 (sec), leaf count = 41
\[\left \{\left \{y(x)\to c_2 \sqrt [3]{x} \text {sn}\left (\left .\left (c_1+\frac {\sqrt {a x^{20/3}}}{\sqrt {2} x^3}\right ) c_2\right |-1\right )\right \}\right \}\]
Maple ✓
cpu = 0.302 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C2} \,\mathrm {sn}\left (\left (\frac {\sqrt {2}\, \sqrt {x^{\frac {20}{3}} a}}{2 x^{3}}+\textit {\_C1} \right ) \textit {\_C2} | i\right ) x^{\frac {1}{3}}\right ]\] Mathematica raw input
DSolve[2*y[x] + a*y[x]^3 + 9*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^(1/3)*C[2]*JacobiSN[(Sqrt[a*x^(20/3)]/(Sqrt[2]*x^3) + C[1])*C[2], -1]}}
Maple raw input
dsolve(9*x^2*diff(diff(y(x),x),x)+a*y(x)^3+2*y(x) = 0, y(x))
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)]