My calculus is just finishing up "Differential Equations" and we have an on-line assignment. I've done all the other questions correctly except for one. It doesn't make sense to me but hopefully someone here can help.

The question is:

Find the solution to the differential equation:

dz/dt = 9te(^6z)

that passes through the origin.

I have gotten the answer:

z= [ln (-27(t^2) - C)]/-6

but I can't figure out how to get C or get the appropriate answer.