Random Forced Exponential Diff Equations

[Gspace]

Homework Statement

I was given three plots of solutions for a forced exponential diffeq: y'[t]+1.85 y[t]=0.7t^2
with starter values on y[0] equal to -6, 0,and +7

The three plots eventually merge, how do I give the formula for this parabola?

Homework Equations

E^(-r t) starter1+E^(-r t) Integral, of E^(rs) f ds

 

[LCKurtz]

The solution isn't a parabola. And you relevant equation isn't correct. It should be

$$y(t) = y(0)e^{-rt} +\int_0^t e^{-rs}f(s)\,ds$$

If you don't know how to solve the equation for yourself you can just plug your information into this equation. (It is common usage to use f(t) instead of f[t] for function notation.)