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**1. Homework Statement**

What do you do if one of the roots to the characteristic equation of a differential equation is zero when using variation of parameters?

**2. Homework Equations**

**3. The Attempt at a Solution**

The problem I encountered this in is

y" - y' = 4t

Characteristic equation

r

^{2}- r = 0

so

r = -1 , 0

Therefore

y

_{1}= e

^{-t}

but

y

_{2}= 0

which would make the Wronskian zero.

Any thoughts?