Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting  in to  and , integrate with respect to time, and then take the derivative with respect to z.
V(z,t)= f+(t-z/vp) + f-(t+z/vp)  where f is some arbitrary function.
∂V/∂z= -L(∂I/∂t) 
∂I/∂z= -C(∂V/∂t) 
The Attempt at a Solution
Ok,so I tried starting with  and integrating with respect to time: ∫(∂I/∂z)∂t= ∫(-C(∂V/∂t))∂t
which gives (I think) V=-1/C ∫(∂I/∂z)∂t
now differentiating this with respect to z: ∂V/∂z= ∂/∂z[-1/C ∫(∂I/∂z)∂t]
and substituting the RHS of this in to :∂/∂z[-1/C ∫(∂I/∂z)∂t]=-L(∂I/∂t)
now I'm stuck and not sure where to go from here. The solution is the well known equation
I(z,t)= (1/Z0)[f+(t-z/vp) + f-(t+z/vp)] where Z0=√(L/C)
I would appreciate knowing the steps to get there.
Thanks very much