# Math Help - Power Law Solution/Initial conditions

1. ## Power Law Solution/Initial conditions

Hi,

I have the following equation as a general solution:

L = k1t^1/3 + k2t^2/3

I need to write down the initial values for L and dl/dt at time t=to.

First question is am i right in thinking that these are: t=0, t=1?

and then will it be obvious how this leads onto

L=L0{2(t/t0)^1/3 - (t/t0)^2/3}

Cheers

2. the initial conditions are at the same time --you want L(t0) and dL/dt(t0)

If you think about it suppose you were doing projectile motion then

you would need the position s(t) and velocity v(t) both at t = 0

For L = k1t^1/3 + k2t^2/3

L(t0) = L0 = k1(t0)^1/3 + k2(t0)^2/3

dL/dt(t0) = 1/3k1(t0)^(-2/3) +2/3k2(t0)^-1/3

do you have any other info on dL/dt(t0) ?

3. no but what u said makes sense thats what I was heading towards just not confident enough to make final step!