[?] Get a solution for a hard spring?

[manjumahee89 (manjunath c)]

need solution for Hard spring

[mthiel (Marco Thiel)]

Something like this?

sols=DSolve[{x''[t] + (1 + a^2 (x[t])^2) x[t] == 0, x[0] == A, x'[0] == 0}, x, t]
(*{{x -> Function[{t}, A JacobiSN[1/2 (-Sqrt[2] Sqrt[2 + a^2 A^2] t + 2 EllipticK[-((a^2 A^2)/(2 + a^2 A^2))]), -((a^2 A^2)/(2 + a^2 A^2))]]}}*)

and then

Plot[(x[t] /. sols[[1]]) /. {A -> 1, a -> 5}, {t, 0, 10}]

All that is modulo typos etc.

Cheers,

Marco