I need help finding the solution to this differential equation.
dz/dt = 9te^(4z)
I cross multiply so that it becomes: dz/e^(4z) = 9t dt
From here I need to integrate.
on the left side, I do substitution and this is what I did:
u = e^(4z)
du = 4e^(4z) dz
du/4e^(4z) = dz
From here, my equation looked like:
du/4ue^(4z) = (9t^2)/2 + C
1/4e^(4z) ln|u| = (9t^2)/2 + C
I subbed in back the u in the absolute brackets but I am unsure of what to do next. I need to sub the points in f(0) = 0 but if I do using my equation, I am going to get 0, which I think is incorrect. Any ideas of where I went wrong?