2.1681   ODE No. 1681

\[ a y(x)^3+9 x^2 y''(x)+2 y(x)=0 \]

Mathematica : cpu = 2.63868 (sec), leaf count = 41

DSolve[2*y[x] + a*y[x]^3 + 9*x^2*Derivative[2][y][x] == 0,y[x],x]
 
\[\left \{\left \{y(x)\to c_2 \sqrt [3]{x} \text {sn}\left (\left .\left (c_1+\frac {\sqrt {a x^{20/3}}}{\sqrt {2} x^3}\right ) c_2\right |-1\right )\right \}\right \}\]

Maple : cpu = 0.056 (sec), leaf count = 31

dsolve(9*x^2*diff(diff(y(x),x),x)+a*y(x)^3+2*y(x)=0,y(x))
 
\[y \left (x \right ) = c_{2} \operatorname {JacobiSN}\left (\left (\frac {\sqrt {2}\, \sqrt {x^{{20}/{3}} a}}{2 x^{3}}+c_{1} \right ) c_{2} , i\right ) x^{{1}/{3}}\]