`assuming`([dsolve({a3(0) = 0, diff(a3(z), z) = -K*a10*a20*sqrt(1-a3(z)^2/a10^2)*sqrt(1-a3(z)^2/a20^2)})], [positive])

which returns

a3(z) = -JacobiSN(z*a10*K, a20/a10)*a20

While in Mathematica, it yields a different solution:

a3(z) = -JacobiSN(z*a10*K, a20^2/a10^2)*a20

Which is right?

Thanks in advance.