Why there is a minus in the power

[electron2]

when the two roots s1 and s2 that are different of the homogenius equation
in normal diff theory i do

$$v_c (t)=Ae^{s_1t}+Be^{s_2t}$$

why why in basic circuit theory we do
$$v_c (t)=Ae^{-|s_1|t}+Be^{-|s_2|t}$$

 

[HallsofIvy]

I'm afraid you'll have to ask that in a "circuit theory" thread. Whatever the reason, It would have to be a physics reason rather than mathematics. I would suspect there is some physical reason why $v_c(t)$ must be decreasing in time. Are the $s_1$ and $s_2$ complex numbers?

 

[electron2]

s1 and s2 are not complex