Quick Question on Variation of Parameters Differential Equations

[colonelone]

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?

Homework Equations

The Attempt at a Solution

The problem I encountered this in is

y" - y' = 4t

Characteristic equation

r² - r = 0

so

r = -1 , 0

Therefore

y₁ = e^-t

but

y₂ = 0

which would make the Wronskian zero.

Any thoughts?

 

[rock.freak667]

Your other solution would be y2=e^(0*t) = 1