ODE
\[ 2 y''(x)=12 y(x)^2+1 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.192236 (sec), leaf count = 14
\[\{\{y(x)\to \wp (x+c_1;-1,c_2)\}\}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 10
\[[y \left (x \right ) = \WeierstrassP \left (x +\textit {\_C1} , -1, \textit {\_C2}\right )]\] Mathematica raw input
DSolve[2*y''[x] == 1 + 12*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> WeierstrassP[x + C[1], {-1, C[2]}]}}
Maple raw input
dsolve(2*diff(diff(y(x),x),x) = 1+12*y(x)^2, y(x))
Maple raw output
[y(x) = WeierstrassP(x+_C1,-1,_C2)]