Differential Equations\ First-order linear differential equation with constant coefficients:\

u

: displacement;

t

: time\ [

u

is a function of

t

\ Given:

a(du)/(dt)+u=0

and

u(0)=u_(0)

\ i) What are the dimensions of

a

?\ ii) If

u(t)=ce^(-st)

is a solution, valid for

t>=0

, then

c=

and

s=

ifferential Equations irst-order linear differential equation with constant coefficients: u : displacement; t : time [ u is a function of t] Given: adtdu+u=0 and u(0)=u0 i) What are the dimensions of a ? ii) If u(t)=cest is a solution, valid for t0, then c= , and s=