Second order system rise time question

[berdan]

Homework Statement

The question is such :
System is modeled as : y''+2y'+4y=u(t)
find the time at which the system goes up 75,90,95 % of its final value.

Homework Equations

The Attempt at a Solution

I have no idea how to touch that,I tried to find the source of the regular rise time (from 10 to 90%),and didn't got it.How the hell do I even start?It looks impossible to isolate expression for time,from PE solution . Also,from the answers in the book,the answers are approximations (t for 75% for example is ~0.9sec).

Thanks in advance.

 

[rude man]

Solve the ODE for y(t) conventionally or use Laplace transforms.

EDIT: looks like an ugly transcendental equation to get t(y) though. Get out the old Excel spreadsheet!

 

[berdan]

Yea,that is the problem,I wanted to know how to do it without any help of mathlab and such,but it looks like overly nasty equation to solve manually (it has exponent of time coupled with sin and cosine terms)
anyway,thanks.

 

[NascentOxygen]

Maybe they just want you to read it off a normalized graph?