Question: How can we get the single possible solution?

I solved the differential equation using 'dsolve' and Maple returns it with fiver possible solutions. How can we get the single possible solution for w(x) if we assume c, g (constants) are positive? Also, can we convert JacobiSN() to a simple trigonometric or algebraic function?




q := (1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

(1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0


dsolve((1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0, {w(x)})

w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = (-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = 2*JacobiSN((1/2)*(-2*c+2*(c^2+2*g)^(1/2))^(1/2)*x+_C1, ((c*(c^2+2*g)^(1/2)-c^2-g)*g)^(1/2)/(c*(c^2+2*g)^(1/2)-c^2-g))*g/(g*(-c+(c^2+2*g)^(1/2)))^(1/2)





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