ODE No. 372

\[ a y(x)+b+y'(x)^2-4 y(x)^3=0 \] Mathematica : cpu = 0.0033538 (sec), leaf count = 27

DSolve[b + a*y[x] - 4*y[x]^3 + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\{\{y(x)\to \wp (x-c_1;a,b)\},\{y(x)\to \wp (x+c_1;a,b)\}\}\] Maple : cpu = 0.047 (sec), leaf count = 232

dsolve(diff(y(x),x)^2-4*y(x)^3+a*y(x)+b = 0,y(x))
 

\[y \left (x \right ) = \frac {\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{6 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}}\]