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 = 0.0489943 (sec), leaf count = 14
\[\left \{\left \{y(x)\to \wp \left (x+c_1;-1,c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.175 (sec), leaf count = 10
\[ \left \{ y \left ( x \right ) ={\it WeierstrassP} \left ( {\it \_C1}+x,-1,{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = WeierstrassP(_C1+x,-1,_C2)