I am trying to solve a differential equation corresponding to a model for visco-elastic material behavior. the model consists of 5 units of spring-dampers placed in parallel and should be solved for the strain \(\displaystyle \varepsilon(t)\). The material is subject to a constant stress \(\displaystyle \sigma_0\). I am able to come-up with a single fifth order differential equation but I am struggling to find the initial conditions. I have found the first initial condition as can be seen in the attached image, but don't know how to come-up with the remaining four conditions. Can anyone help me solve this problem?

Thanks in advance!

Joa